1. Equations & Inequalities

Linear Inequalities

1. Equations & Inequalities

Linear Inequalities

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Multiple Choice

Solve the inequality. Express the solution set in interval notation and graph. $2x+12>19$

$\left(-\infty,\frac72\right)$

A number line with a graph

$\left(-\infty,\frac72\right]$

A number line with a graph

$\left[\frac72,\infty\right)$

A number line with a graph

$\left(\frac72,\infty\right)$

A number line with a graph

Verified step by step guidance

Start by isolating the variable on one side of the inequality. Given the inequality $2x + 12 > 19$, subtract 12 from both sides to get $2x > 7$.

Next, divide both sides of the inequality by 2 to solve for $x$. This gives $x > \frac{7}{2}$.

Express the solution set in interval notation. Since $x$ is greater than $\frac{7}{2}$, the interval notation is $(\frac{7}{2}, \infty)$.

To graph the solution, draw a number line. Mark $\frac{7}{2}$ on the number line and use an open circle to indicate that $\frac{7}{2}$ is not included in the solution set.

Shade the region to the right of $\frac{7}{2}$ to represent all values greater than $\frac{7}{2}$. This visualizes the solution $(\frac{7}{2}, \infty)$.