Question

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Answer 1

$\sf \frac { 7 x - 1 } { 4 } - \frac { 1 } { 7 } ( 2 x - \frac { 1 - x } { 2 } ) = 4$

Multiply both sides of the equation by 28, the least common multiple of 4,7,2.

$\sf 7\left(7x-1\right)-4\left(2x-\frac{1-x}{2}\right)=112$

Use the distributive property to multiply 7 by 7x - 1.

$\sf 49x-7-4\left(2x-\frac{1-x}{2}\right)=112$

Divide each term of 1 - x by 2 to get $\sf \frac{1}{2}-\frac{1}{2}x$

$\sf 49x-7-4\left(2x-\left(\frac{1}{2}-\frac{1}{2}x\right)\right)=112$

To find the opposite of $\sf \frac{1}{2}-\frac{1}{2}x$, find the opposite of each term.

The opposite of $\sf -\frac{1}{2}x \: \: is \: \: \frac{1}{2}x$

$\sf 49x-7-4\left(2x-\frac{1}{2}+\frac{1}{2}x\right)=112$

Combine 2x and $\sf \frac{1}{2}x$ to get $\sf \frac{5}{2}x$.

$\sf 49x-7-4\left(\frac{5}{2}x-\frac{1}{2}\right)=112$

Use the distributive property to multiply -4 by $\sf \frac{5}{2}x-\frac{1}{2}$

$\sf 49x-7-4\times \left(\frac{5}{2}\right)x-4\left(-\frac{1}{2}\right)=112$

Express $\sf -4\times \left(\frac{5}{2}\right)$ as a single fraction.

$\sf 49x-7+\frac{-4\times 5}{2}x-4\left(-\frac{1}{2}\right)=112$

Multiply -4 and 5 to get -20.

$\sf 49x-7+\frac{-20}{2}x-4\left(-\frac{1}{2}\right)=112$

Divide -20 by 2 to get -10.

$\sf 49x-7-10x-4\left(-\frac{1}{2}\right)=112$

Express $\sf -4\left(-\frac{1}{2}\right)$ as a single fraction.

$\sf 49x-7-10x+\frac{-4\left(-1\right)}{2}=112$

Multiply -4 and -1 to get 4.

$\sf 49x-7-10x+\frac{4}{2}=112$

Divide 4 by 2 to get 2.

$\sf 49x-7-10x+2=112$

Combine 49x and -10x to get 39x.

$\sf 39x-7+2=112$

Add -7 and 2 to get -5.

$\sf 39x-5=112$

Add 5 to both sides.

$\sf 39x=112+5$

Add 112 and 5 to get 117.

$\sf 39x=117$

Divide both sides by 39.

$\sf x=\frac{117}{39}$

Divide 117 by 39 to get 3.

$\sf \underline{x=3 }$

I hope it helps you ❤️✔️