2. Linear Equations and Inequalities

Set Operations and Compound Inequalities

2. Linear Equations and Inequalities

Set Operations and Compound Inequalities

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Multiple Choice

Solve the following inequalities and express the answer in interval notation.
$- 4 \leq 2 x + 1 \leq 7$

$\left\lbrack-6,8\right\rbrack$

$\left\lbrack-\frac32,4\right\rbrack$

$\left\lbrack-\frac52,3\right\rbrack$

$\left\lbrack-10,6\right\rbrack$

Verified step by step guidance

Start with the compound inequality: $-4 \leq 2x + 1 \leq 7$.

Subtract 1 from all three parts of the inequality to isolate the term with $x$: $-4 - 1 \leq 2x + 1 - 1 \leq 7 - 1$, which simplifies to $-5 \leq 2x \leq 6$.

Divide all parts of the inequality by 2 to solve for $x$: $\frac{-5}{2} \leq x \leq \frac{6}{2}$.

Simplify the fractions to get the solution in terms of $x$: $-\frac{5}{2} \leq x \leq 3$.

Express the solution in interval notation as $\left[ -\frac{5}{2}, 3 \right]$, indicating that $x$ includes both endpoints.

4:56m

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Struggling with Intermediate Algebra?

Solve the following inequalities and express the answer in interval notation.−4≤2x+1≤7-4\le2x+1\le7

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Solve the following inequalities and express the answer in interval notation.
$- 4 \leq 2 x + 1 \leq 7$