1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$\frac { 2 x + 3 } { 3 } + \frac { x - 1 } { 2 } + \frac { 2 x } { 4 } = 8$$

Solve for x

$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$

Steps for Solving Linear Equation

Multiply both sides of the equation by $12$, the least common multiple of $3,2,4$.

$$4\left(2x+3\right)+6\left(x-1\right)+3\times 2x=96$$

Use the distributive property to multiply $4$ by $2x+3$.

$$8x+12+6\left(x-1\right)+3\times 2x=96$$

Use the distributive property to multiply $6$ by $x-1$.

$$8x+12+6x-6+3\times 2x=96$$

Combine $8x$ and $6x$ to get $14x$.

$$14x+12-6+3\times 2x=96$$

Subtract $6$ from $12$ to get $6$.

$$14x+6+3\times 2x=96$$

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

$$14x+6+6x=96$$

Combine $14x$ and $6x$ to get $20x$.

$$20x+6=96$$

Subtract $6$ from both sides.

$$20x=96-6$$

Subtract $6$ from $96$ to get $90$.

$$20x=90$$

Divide both sides by $20$.

$$x=\frac{90}{20}$$

Reduce the fraction $\frac{90}{20}$ to lowest terms by extracting and canceling out $10$.

$$x=\frac{9}{2}$$

Show Solution