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Question Solve for x in the linear equation 3(x−4)=−93(x-4)=-9.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 3(x−4)=−93(x-4)=-9.
2. We need to solve for the variable xx.

STEP 2

First, we need to distribute the 33 across the terms inside the parentheses.
3(x−4)=3x−3⋅43(x-4) = 3x - 3 \cdot 4

STEP 3

Perform the multiplication to simplify the expression.
3x−3⋅4=3x−123x - 3 \cdot 4 = 3x - 12

STEP 4

Now, rewrite the equation with the simplified expression.
3x−12=−93x - 12 = -9

STEP 5

Next, we need to isolate the variable xx on one side of the equation. We can do this by adding 1212 to both sides of the equation to cancel out the −12-12.
3x−12+12=−9+123x - 12 + 12 = -9 + 12

STEP 6

Simplify both sides of the equation.
3x=33x = 3

STEP 7

Now, divide both sides of the equation by 33 to solve for xx.
3x3=33\frac{3x}{3} = \frac{3}{3}

STEP 8

Perform the division to find the value of xx.
x=1x = 1
The solution to the equation 3(x−4)=−93(x-4)=-9 is x=1x = 1.

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