Solve x+a-4/x+3*8=3/4

$$\frac { x + a - 4 } { x + 3 \cdot 8 } = \frac { 3 } { 4 }$$

Solve for a

$$a=-\frac{x}{4}+22$$

$$x\neq -24$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(x+24\right), the least common multiple of x+3\times 8,4.

$$4\left(x+a-4\right)=3\left(x+24\right)$$

Use the distributive property to multiply 4 by x+a-4.

$$4x+4a-16=3\left(x+24\right)$$

Use the distributive property to multiply 3 by x+24.

$$4x+4a-16=3x+72$$

Subtract 4x from both sides.

$$4a-16=3x+72-4x$$

Combine 3x and -4x to get -x.

$$4a-16=-x+72$$

Add 16 to both sides.

$$4a=-x+72+16$$

Add 72 and 16 to get 88.

$$4a=-x+88$$

The equation is in standard form.

$$4a=88-x$$

Divide both sides by 4.

$$\frac{4a}{4}=\frac{88-x}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a=\frac{88-x}{4}$$

Divide -x+88 by 4.

$$a=-\frac{x}{4}+22$$

Solve for x

$$x=88-4a$$

$$a\neq 28$$

Solution Steps

Variable x cannot be equal to -24 since division by zero is not defined. Multiply both sides of the equation by 4\left(x+24\right), the least common multiple of x+3\times 8,4.

$$4\left(x+a-4\right)=3\left(x+24\right)$$

Use the distributive property to multiply 4 by x+a-4.

$$4x+4a-16=3\left(x+24\right)$$

Use the distributive property to multiply 3 by x+24.

$$4x+4a-16=3x+72$$

Subtract 3x from both sides.

$$4x+4a-16-3x=72$$

Combine 4x and -3x to get x.

$$x+4a-16=72$$

Subtract 4a from both sides.

$$x-16=72-4a$$

Add 16 to both sides.

$$x=72-4a+16$$

Add 72 and 16 to get 88.

$$x=88-4a$$

Variable x cannot be equal to -24.

$$x=88-4a\text{, }x\neq -24$$