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Math  /  Algebra

Question−4=3+7(x−1)-4=3+7(x-1)

Studdy Solution

STEP 1

1. The equation −4=3+7(x−1) -4 = 3 + 7(x - 1) is asking us to solve for x x .
2. This is a linear equation involving distribution and basic algebraic operations.
3. The goal is to isolate the variable x x .

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable x x by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 7 7 across the terms inside the parentheses:
−4=3+7x−7 -4 = 3 + 7x - 7

STEP 4

Combine like terms on the right side of the equation:
−4=7x−4 -4 = 7x - 4

STEP 5

Add 4 4 to both sides of the equation to begin isolating 7x 7x :
−4+4=7x−4+4 -4 + 4 = 7x - 4 + 4
Simplify:
0=7x 0 = 7x

STEP 6

Divide both sides by 7 7 to solve for x x :
07=7x7 \frac{0}{7} = \frac{7x}{7}
Simplify:
0=x 0 = x

STEP 7

Check the solution by substituting x=0 x = 0 back into the original equation:
−4=3+7(0−1) -4 = 3 + 7(0 - 1)
Simplify the right side:
−4=3−7 -4 = 3 - 7
−4=−4 -4 = -4
Both sides are equal, confirming the solution is correct.
The solution is:
0 \boxed{0}

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