Algebra Examples

$4 (x - 2) + 3 (x + 1) = 3 (x - 1)$

Step 1

Simplify $4 (x - 2) + 3 (x + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 x + 4 \cdot - 2 + 3 (x + 1) = 3 (x - 1)$

Step 1.1.2

Multiply $4$ by $- 2$ .

$4 x - 8 + 3 (x + 1) = 3 (x - 1)$

Step 1.1.3

Apply the distributive property.

$4 x - 8 + 3 x + 3 \cdot 1 = 3 (x - 1)$

Step 1.1.4

Multiply $3$ by $1$ .

$4 x - 8 + 3 x + 3 = 3 (x - 1)$

$4 x - 8 + 3 x + 3 = 3 (x - 1)$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $4 x$ and $3 x$ .

$7 x - 8 + 3 = 3 (x - 1)$

Step 1.2.2

Add $- 8$ and $3$ .

$7 x - 5 = 3 (x - 1)$

$7 x - 5 = 3 (x - 1)$

$7 x - 5 = 3 (x - 1)$

Step 2

Simplify $3 (x - 1)$ .

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Step 2.1

Apply the distributive property.

$7 x - 5 = 3 x + 3 \cdot - 1$

Step 2.2

Multiply $3$ by $- 1$ .

$7 x - 5 = 3 x - 3$

$7 x - 5 = 3 x - 3$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $3 x$ from both sides of the equation.

$7 x - 5 - 3 x = - 3$

Step 3.2

Subtract $3 x$ from $7 x$ .

$4 x - 5 = - 3$

$4 x - 5 = - 3$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $5$ to both sides of the equation.

$4 x = - 3 + 5$

Step 4.2

Add $- 3$ and $5$ .

$4 x = 2$

$4 x = 2$

Step 5

Divide each term in $4 x = 2$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{4}$

$x = \frac{2}{4}$

$x = \frac{2}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $2$ and $4$ .

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Step 5.3.1.1

Factor $2$ out of $2$ .

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

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

$x = \frac{1}{2}$

$x = \frac{1}{2}$

$x = \frac{1}{2}$

$x = \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$