Algebra questions with remedies and Explanations because that Grade 9

Detailed solutions and full explanations come grade 9 algebra questions are presented.

You are watching: Solve for x if 2(5x + 2)2 = 48.


Simplify the adhering to algebraic expressions.- 6x + 5 + 12x -6 2(x - 9) + 6(-x + 2) + 4x3x2 + 12 + 9x - 20 + 6x2 - x (x + 2)(x + 4) + (x + 5)(-x - 1) 1.2(x - 9) - 2.3(x + 4)(x2y)(xy2)(-x2y2)(xy2)SolutionGroup choose terms and simplify.- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - 6)= 6x - 1Expand brackets.2(x - 9) + 6(-x + 2) + 4x = 2x - 18 - 6x + 12 + 4xGroup favor terms and simplify.= (2x - 6x + 4x) + (- 18 + 12) = - 6Group choose terms and simplify.3x2 + 12 + 9x - 20 + 6x2 - x= (3x2 + 6x2) + (9x - x) + (12 - 20)= 9x2 + 8x - 8Expand brackets.(x + 2)(x + 4) + (x + 5)(- x - 1)= x2 + 4x + 2x + 8 - x2 - x - 5x - 5Group favor terms.= (x2 - x2) + (4x + 2x - x - 5x) + (8 - 5)= 3Expand and also group.1.2(x - 9) - 2.3(x + 4)= 1.2x - 10.8 - 2.3x - 9.2= -1.1x - 20Rewrite as follows.(x2y)(xy2) = (x2 x)(y y2)Use rules of exponential.= x3 y3Rewrite expression as follows.(-x2y2)(xy2) = -(x2 x)( y2 y2)Use rule of exponential.= - x3 y4

Simplify the expressions.(a b2)(a3 b) / (a2 b3)(21 x5) / (3 x4)(6 x4)(4 y2) / < (3 x2)(16 y) > (4x - 12) / 4 (-5x - 10) / (x + 2)(x2 - 4x - 12) / (x2 - 2 x - 24)
SolutionUse rule of exponential to simplify the numerator first.(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)Rewrite together follows.(a4 / a2) (b3 / b3)Use ascendancy of quotient of exponentials to simplify.= a2 Rewrite together follows.(21 x5) / (3 x4) = (21 / 3)(x5 / x4)Simplify.= 7 x(6 x4)(4 y2) / < (3 x2)(16 y) >Multiply state in numerator and denominator and simplify.(6 x4)(4 y2) / < (3 x2)(16 y) > = (24 x4 y2) / (48 x2 y)Rewrite as follows.= (24 / 48)(x4 / x2)(y2 / y)Simplify.= (1 / 2) x2 yFactor 4 out in the numerator.(4x - 12) / 4 = 4(x - 3) / 4Simplify.= x - 3Factor -5 out in the numerator.(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)Simplify.= - 5Factor numerator and denominator together follows.(x2 - 4x - 12) / (x2 - 2x - 24) = <(x - 6)(x + 2)> / <(x - 6)(x + 4)>Simplify.= (x + 2) / (x + 4) , for all x no equal to 6

Solve because that x the adhering to linear equations. 2x = 6 6x - 8 = 4x + 4 4(x - 2) = 2(x + 3) + 7 0.1 x - 1.6 = 0.2 x + 2.3 - x / 5 = 2 (x - 4) / (- 6) = 3 (-3x + 1) / (x - 2) = -3 x / 5 + (x - 1) / 3 = 1/5SolutionDivide both political parties of the equation through 2 and also simplify.2x / 2 = 6 / 2x = 3Add 8 to both sides and also group prefer terms.6x - 8 + 8 = 4x + 4 + 86x = 4x + 12Add - 4x to both sides and also group choose terms.6x - 4x = 4x + 12 - 4x2x = 12Divide both sides by 2 and simplify.x = 6Expand brackets.4x - 8 = 2x + 6 + 7Add 8 to both sides and also group like terms.4x - 8 + 8 = 2x + 6 + 7 + 84x = 2x + 21Add - 2x to both sides and also group favor terms.4x - 2x = 2x + 21 - 2x2x = 21Divide both political parties by 2.x = 21 / 2Add 1.6 come both sides and simplify.0.1 x - 1.6 = 0.2 x + 2.30.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.60.1 x = 0.2 x + 3.9Add - 0.2 x to both sides and simplify.0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x- 0.1 x = 3.9Divide both political parties by - 0.1 and simplify.x = - 39Multiply both political parties by - 5 and also simplify.- 5(- x / 5) = - 5(2)x = - 10Multiply both political parties by - 6 and also simplify.(-6)(x - 4) / (- 6) = (-6)3x - 4 = - 18Add 4 to both sides and also simplify.x = - 14Multiply both sides by (x - 2) and also simplify.(x - 2)(-3x + 1) / (x - 2) = -3(x - 2)Expand best term.-3x + 1 = -3x + 6Add 3x to both sides and simplify.- 3x + 1 + 3x = - 3x + 6 + 3x1 = 6The critical statement is false and also the equation has no solutions.Multiply every terms by the LCM the 5 and also 3 i m sorry is 15.15(x / 5) + 15(x - 1) / 3 = 15(1 / 5)Simplify and expand.3x + 15x - 15 = 3Group favor terms and also solve.18 x = 3 + 1518 x = 18x = 1

Find any real options for the adhering to quadratic equations.2 x2 - 8 = 0x2 = -52x2 + 5x - 7 = 0 (x - 2)(x + 3) = 0 (x + 7)(x - 1) = 9 x(x - 6) = -9SolutionDivide all terms through 2.2 x2 / 2 - 8 / 2 = 0 / 2and simplifyx2 - 4 = 0Factor the appropriate side.(x - 2)(x + 2) = 0Solve for x.x - 2 = 0 or x = 2x + 2 = 0 or x = -2Solution collection -2 , 2The provided equationx2 = -5 has no real solution since the square of genuine numbers is never negative.Factor the left side as follows.2x2 + 5x - 7 = 0Factor(2x + 7)(x - 1) = 0Solve because that x.2x + 7 = 0 or x - 1 = 0x = - 7/2 , x = 1, solution set:-7/2 , 1Solve because that x.(x - 2)(x + 3) = 0x - 2 = 0 or x + 3 = 0solution set: -3 , 2Expand left side.x2 + 6x - 7 = 9Rewrite the over equation with best side equal to 0.x2 + 6x - 16 = 0Factor left side.(x + 8)(x - 2) = 0Solve for x.x + 8 = 0 or x - 2 = 0solution set: -8 , 2Expand left side and also rewrite with right side same to zero.x2 - 6x + 9 = 0Factor left side.(x - 3)2 = 0Solve for x.x - 3 = 0solution set: 3

Find any kind of real solutions for the complying with equations.x3 - 1728 = 0x3 = - 64 √x = -1 √x = 5 √(x/100) = 4 √(200/x) = 2SolutionRewrite equation as.x3 = 1728Take the cube source of each side.(x3)1/3 = (1728)1/3Simplify.x = (1728)1/3 = 12Take the cube root of every side.(x3)1/3 = (- 64)1/3Simplify.x = - 4 The equation √x= - 1 has no actual solution because the square of a actual number is better than or equal to zero.Square both sides.(√x)2 = 52Simplify.x = 25Square both sides.(√(x/100))2 = 42Simplify.x / 100 = 16Multiply both sides by 100 and also simplify.x = 1,600Square both sides.(√(200/x))2 = 22Simplify.200 / x = 4Multiply both sides by x and also simplify.x(200 / x) = 4 x200 = 4 xSolve for x.x = 50

Evaluate because that the given values the a and b.a2 + b2 , for a = 2 and b = 2|2a - 3b| , because that a = -3 and also b = 53a3 - 4b4 , for a = -1 and also b = -2SolutionSubstitute a and also b by your values and evaluate.for a = 2 and also b = 2a2 + b2 = 22 + 22 = 8 set a = - 3 and b = 5 in the given expression and evaluate.| 2a - 3b | = | 2( -3) - 3(5) | = | -6 - 15 | = | -21 | = 21Set a = - 1 and b = -2 in the provided expression and also evaluate.3a3 - 4b4 = 3(-1)3 - 4(-2)4 = 3(-1) - 4(16) = - 3 - 64 = - 67

Solve the adhering to inequalities. X + 3 x + 1 > -x + 5 2(x - 2) SolutionAdd -3 come both sides of the inequality and simplify.x + 3 - 3 x add x come both political parties of the inequality and also simplify.x + 1 + x > - x + 5 + x2x + 1 > 5Add -1 come both political parties of the inequality and simplify.2x + 1 - 1 > 5 - 12x > 4Divide both political parties by 2.x > 2Expand brackets and also group prefer terms.2x - 4 include 4 to both sides and also simplify.2x - 4 + 4 2x include x to both sides and also simplify.2x + x 3x division both political parties by 3 and simplify.x

For what worth of the consistent k
walk the quadratic equation x2 +2x = - 2k have two distinctive real solutions?SolutionWe first find write the given equation with appropriate side equal to zero.x2 +2x + 2k = 0We currently calculate the discriminant D that the quadratic equation.D = b2 - 4 a c = 22 - 4 (1)(2k) = 4 - 8 kFor the solution to have actually two distinctive real solution, D needs to be positive. Hence4 - 8 k > 0Solve the inequality to getk

For what value of the constant b
go the direct equation 2 x + b y = 2 have a slope equal to 2?SolutionSolve because that y and identify the slopeb y = - 2 x + 2y = (- 2 / b) x + 2 / bslope = (- 2 / b) = 2Solve the equation (- 2 / b) = 2for b(- 2 / b) = 2-2 = 2 bb = - 1

What is the y intercept of the line - 4 x + 6 y = - 12
?SolutionSet x = 0 in the equation and also solve for y.- 4 (0) + 6 y = - 126 y = - 12y = - 2y intercept: (0 , - 2)

What is the x intercept of the heat - 3 x + y = 3
?SolutionSet y = 0 in the equation and also solve because that x.- 3 x + 0 = 3x = -1x intercept: (-1 , 0)

What is allude of intersection the the present x - y = 3
and - 5 x - 2 y = - 22?SolutionA suggest of intersection of two lines is solution to the equations of both lines. To uncover the allude of intersection of the 2 lines, we need to solve the system of equations x - y = 3 and also -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be fixed for x to givex = 3 + ySubstitute x through 3 + y in the equation - 5 x - 2 y = -22 and also solve because that y-5 (3 + y) - 2 y = - 22-15 - 5 y - 2 y = - 22-7 y = - 22 + 15-7 y = - 7y = 1Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and also solve for yx = 3 + y = 3 + 1 = 4Point the intersection: (4 , 1)

For what value of the continuous k
does the line - 4 x + k y = 2 pass with the allude (2,-3)?SolutionFor the line to pass v the allude (2,-3), the ordered pair (2,-3) have to be a systems to the equation of the line. Us substitute x by 2 abd y by - 3 in the equation. - 4(2) + k(-3) = 2Solve the because that k to obtaink = - 10 / 3

What is the steep of the line through equation y - 4 = 10
?Solution compose the offered equation in steep intercept type y = m x + b and also identify the steep m. Y = 14It is a horizontal line and therefore the steep is equal to 0.

What is the steep of the line through equation 2 x = -8
?Solution The above equation may be created as x = - 4It is a vertical line and also therefore the slope is undefined.

Find the x and also y intercepts of the line through equation x = - 3
?Solution The above is a upright line with x intercept only provided by (-3 , 0)

Find the x and y intercepts that the line with equation 3 y - 6 = 3
?SolutionThe given equation may be composed asy = 3 The above is a horizontal line v y intercept only offered by (0 , 3)

What is the slope of a heat parallel come the x axis?SolutionA heat parallel to the x axis is a horizontal line and also its slope is same to 0.

See more: Is Ribose A Ketose Or Aldose And Ketose? Is Ribose A Ketose

What is the slope of a line perpendicular to the x axis?SolutionA line perpendicular to the x axis is a upright line and its steep is undefined.