1. Equations and Inequalities

Linear Inequalities

1. Equations and 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 simplify the expression.

After subtracting 12 from both sides, the inequality becomes 2x > 7.

Next, divide both sides of the inequality by 2 to solve for x. This gives x > 7/2.

Express the solution set in interval notation. Since x is greater than 7/2, the interval notation is (7/2, ∞).

To graph the solution, draw a number line and mark an open circle at 7/2 to indicate that 7/2 is not included in the solution set. Shade the region to the right of 7/2 to represent all numbers greater than 7/2.