Pre-Algebra Examples

$3 x + \frac{1}{2} y < 2$

Step 1

Solve for $y$ .

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Step 1.1

Combine $\frac{1}{2}$ and $y$ .

$3 x + \frac{y}{2} < 2$

Step 1.2

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

$\frac{y}{2} < 2 - 3 x$

Step 1.3

Multiply both sides by $2$ .

$\frac{y}{2} \cdot 2 < (2 - 3 x) \cdot 2$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $2$ .

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Step 1.4.1.1.1

Cancel the common factor.

$\frac{y}{2} \cdot 2 < (2 - 3 x) \cdot 2$

Step 1.4.1.1.2

Rewrite the expression.

$y < (2 - 3 x) \cdot 2$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $(2 - 3 x) \cdot 2$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y < 2 \cdot 2 - 3 x \cdot 2$

Step 1.4.2.1.2

Simplify the expression.

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Step 1.4.2.1.2.1

Multiply $2$ by $2$ .

$y < 4 - 3 x \cdot 2$

Step 1.4.2.1.2.2

Multiply $2$ by $- 3$ .

$y < 4 - 6 x$

Step 1.4.2.1.2.3

Reorder $4$ and $- 6 x$ .

$y < - 6 x + 4$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 6$

$b = 4$

Step 2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 6$

y-intercept: $(0, 4)$

Slope: $- 6$

y-intercept: $(0, 4)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 6 x + 4$ .

$y < - 6 x + 4$

Step 4