2. Linear Equations and Inequalities

Set Operations and Compound Inequalities

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Multiple Choice

Solve the following inequalities and graph the solution.
$- 6 < 2 x - 4 < 4$

Number line from -8 to 8 with a red bracket highlighting the interval from -1 to 4.

Number line from -8 to 8 with a red line segment and open circles highlighting the interval between -3 and 1.

Number line from -8 to 8 with a red open interval highlighted between -5 and 0.

Number line from -8 to 8 with the interval between 0 and 5 highlighted in red parentheses.

Verified step by step guidance

Start with the compound inequality: $-6 < 2x - 4 < 4$.

Add 4 to all three parts of the inequality to isolate the term with $x$: $-6 + 4 < 2x - 4 + 4 < 4 + 4$, which simplifies to $-2 < 2x < 8$.

Divide all parts of the inequality by 2 to solve for $x$: $\frac{-2}{2} < \frac{2x}{2} < \frac{8}{2}$, which simplifies to $-1 < x < 4$.

Interpret the solution $-1 < x < 4$ as all $x$ values strictly between -1 and 4, not including -1 and 4 themselves.

Graph this solution on the number line by drawing an open interval (parentheses) from -1 to 4, indicating that the endpoints are not included.

Master Intersection and Union of Sets with a bite sized video explanation from Patrick Ford

Solve the following inequalities and graph the solution.−6<2x−4<4-6<2x-4<4