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QuestionSolve the equation: 2[2(3−5x)+4]=5[2(3−3x)+2]2[2(3-5 x)+4]=5[2(3-3 x)+2].

Studdy Solution

STEP 1

Assumptions1. The given equation is [(3−5x)+4]=5[(3−3x)+][(3-5x)+4]=5[(3-3x)+] . We are to solve for xx

STEP 2

First, we need to distribute the numbers outside the brackets to the terms inside the brackets on both sides of the equation.
2[2(−5x)+4]=2[2∗−2∗5x+4]2[2(-5x)+4] =2[2* -2*5x +4]5[2(−x)+2]=5[2∗−2∗x+2]5[2(-x)+2] =5[2* -2*x +2]

STEP 3

Perform the multiplication operations.
2[2∗3−2∗5x+]=2[6−10x+]2[2*3 -2*5x +] =2[6 -10x +]5[2∗3−2∗3x+2]=5[6−6x+2]5[2*3 -2*3x +2] =5[6 -6x +2]

STEP 4

implify the expressions inside the brackets.
2[6−10x+4]=2[10−10x]2[6 -10x +4] =2[10 -10x][6−6x+2]=[8−6x][6 -6x +2] =[8 -6x]

STEP 5

Next, distribute the numbers outside the brackets to the terms inside the brackets.
2[10−10x]=20−20x2[10 -10x] =20 -20x5[8−x]=40−30x5[8 -x] =40 -30x

STEP 6

We now have a simplified equation.
20−20x=40−30x20 -20x =40 -30x

STEP 7

Next, we isolate the variable xx on one side of the equation. We can do this by adding 20x20x to both sides of the equation.
20−20x+20x=40−30x+20x20 -20x +20x =40 -30x +20x

STEP 8

implify the equation.
20=40−10x20 =40 -10x

STEP 9

To isolate xx, subtract 4040 from both sides of the equation.
20−40=40−x−4020 -40 =40 -x -40

STEP 10

implify the equation.
−20=−10x-20 = -10x

STEP 11

Finally, to solve for xx, divide both sides of the equation by −10-10.
x=−20/−10x = -20 / -10

STEP 12

Calculate the value of xx.
x=−20/−10=2x = -20 / -10 =2So, the solution to the equation is x=2x =2.

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