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Math  /  Algebra

QuestionSolve the equation. 3(2w−7)=33(2 w-7)=3 CLEAR CHECK w=4w=4 w=53w=\frac{5}{3}
w=−15w=-\frac{1}{5} w=75w=\frac{7}{5}

Studdy Solution

STEP 1

1. The equation 3(2w−7)=3 3(2w - 7) = 3 is a linear equation in one variable.
2. We need to solve for w w .
3. The given options are potential solutions: w=4 w = 4 , w=53 w = \frac{5}{3} , w=−15 w = -\frac{1}{5} , w=75 w = \frac{7}{5} .

STEP 2

1. Distribute the constant outside the parentheses.
2. Simplify the equation.
3. Isolate the variable w w .
4. Check the solution by substituting it back into the original equation.
5. Compare the solution with the given options.

STEP 3

Distribute the 3 3 across the terms inside the parentheses:
3×(2w−7)=3 3 \times (2w - 7) = 3
This becomes:
6w−21=3 6w - 21 = 3

STEP 4

Add 21 21 to both sides of the equation to simplify:
6w−21+21=3+21 6w - 21 + 21 = 3 + 21
This simplifies to:
6w=24 6w = 24

STEP 5

Divide both sides by 6 6 to solve for w w :
6w6=246 \frac{6w}{6} = \frac{24}{6}
This simplifies to:
w=4 w = 4

STEP 6

Check the solution by substituting w=4 w = 4 back into the original equation:
3(2(4)−7)=3 3(2(4) - 7) = 3
Simplify inside the parentheses:
3(8−7)=3 3(8 - 7) = 3
3(1)=3 3(1) = 3
The left-hand side equals the right-hand side, confirming the solution is correct.

STEP 7

Compare the solution w=4 w = 4 with the given options:
The correct solution is:
4 \boxed{4}

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