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Math  /  Algebra

Question实 7 Solve for ff 4+10f=7(2f−4)f=□\begin{array}{l} 4+10 f=7(2 f-4) \\ f=\square \end{array}

Studdy Solution

STEP 1

1. The equation 4+10f=7(2f−4) 4 + 10f = 7(2f - 4) is asking us to solve for f f .
2. This is a linear equation with one variable.
3. The equation involves basic algebraic operations, including distribution and combining like terms.

STEP 2

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

STEP 3

Distribute the 7 7 on the right-hand side of the equation:
4+10f=7×2f−7×4 4 + 10f = 7 \times 2f - 7 \times 4
Simplify the right-hand side:
4+10f=14f−28 4 + 10f = 14f - 28

STEP 4

Move all terms involving f f to one side of the equation and constant terms to the other side. Subtract 10f 10f from both sides:
4=14f−10f−28 4 = 14f - 10f - 28
Simplify:
4=4f−28 4 = 4f - 28

STEP 5

Add 28 28 to both sides to isolate the term with f f :
4+28=4f 4 + 28 = 4f
Simplify:
32=4f 32 = 4f

STEP 6

Divide both sides by 4 4 to solve for f f :
324=f \frac{32}{4} = f
Simplify:
f=8 f = 8

STEP 7

Check the solution by substituting f=8 f = 8 back into the original equation:
Original equation: 4+10f=7(2f−4) 4 + 10f = 7(2f - 4)
Substitute f=8 f = 8 :
4+10(8)=7(2(8)−4) 4 + 10(8) = 7(2(8) - 4)
Simplify both sides:
Left-hand side: 4+80=84 4 + 80 = 84
Right-hand side: 7(16−4)=7×12=84 7(16 - 4) = 7 \times 12 = 84
Both sides are equal, confirming the solution is correct.
The solution is:
8 \boxed{8}

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