Solve 3/4 * (7x - 1) - (2x - (1 - x)/2) = x + 1 1/2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{3}{4}(7x-1)-(2x-\frac{1-x}{2})=x+1\frac{1}{2}$$

Solve for x

$x=1$

Steps for Solving Linear Equation

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

$$3\left(7x-1\right)-4\left(2x-\frac{1-x}{2}\right)=4x+2\left(1\times 2+1\right)$$

Use the distributive property to multiply $3$ by $7x-1$.

$$21x-3-4\left(2x-\frac{1-x}{2}\right)=4x+2\left(1\times 2+1\right)$$

Multiply $1$ and $2$ to get $2$.

$$21x-3-4\left(2x-\frac{1-x}{2}\right)=4x+2\left(2+1\right)$$

Add $2$ and $1$ to get $3$.

$$21x-3-4\left(2x-\frac{1-x}{2}\right)=4x+2\times 3$$

Multiply $2$ and $3$ to get $6$.

$$21x-3-4\left(2x-\frac{1-x}{2}\right)=4x+6$$

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

$$21x-3-4\left(2x-\left(\frac{1}{2}-\frac{1}{2}x\right)\right)=4x+6$$

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

$$21x-3-4\left(2x-\frac{1}{2}-\left(-\frac{1}{2}x\right)\right)=4x+6$$

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

$$21x-3-4\left(2x-\frac{1}{2}+\frac{1}{2}x\right)=4x+6$$

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

$$21x-3-4\left(\frac{5}{2}x-\frac{1}{2}\right)=4x+6$$

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

$$21x-3-4\times \frac{5}{2}x-4\left(-\frac{1}{2}\right)=4x+6$$

Express $-4\times \frac{5}{2}$ as a single fraction.

$$21x-3+\frac{-4\times 5}{2}x-4\left(-\frac{1}{2}\right)=4x+6$$

Multiply $-4$ and $5$ to get $-20$.

$$21x-3+\frac{-20}{2}x-4\left(-\frac{1}{2}\right)=4x+6$$

Divide $-20$ by $2$ to get $-10$.

$$21x-3-10x-4\left(-\frac{1}{2}\right)=4x+6$$

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

$$21x-3-10x+\frac{-4\left(-1\right)}{2}=4x+6$$

Multiply $-4$ and $-1$ to get $4$.

$$21x-3-10x+\frac{4}{2}=4x+6$$

Divide $4$ by $2$ to get $2$.

$$21x-3-10x+2=4x+6$$

Combine $21x$ and $-10x$ to get $11x$.

$$11x-3+2=4x+6$$

Add $-3$ and $2$ to get $-1$.

$$11x-1=4x+6$$

Subtract $4x$ from both sides.

$$11x-1-4x=6$$

Combine $11x$ and $-4x$ to get $7x$.

$$7x-1=6$$

Add $1$ to both sides.

$$7x=6+1$$

Add $6$ and $1$ to get $7$.

$$7x=7$$

Divide both sides by $7$.

$$x=\frac{7}{7}$$

Divide $7$ by $7$ to get $1$.

$$x=1$$