Questions: HW Unit 1 - Linear Inequalities Question 22 of 38 (1 point) Question Attempt: 1 of Unlimited Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers. -11 > 6(x-4) + 7 Part: 0 / 3 Part 1 of 3 The solution set in set-builder notation is

HW Unit 1 - Linear Inequalities Question 22 of 38 (1 point) Question Attempt: 1 of Unlimited Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers. -11 > 6(x-4) + 7 Part: 0 / 3 Part 1 of 3 The solution set in set-builder notation is
Transcript text: HW Unit 1 - Linear Inequalities Question 22 of 38 (1 point) | Question Attempt: 1 of Unlimited Solve the inequality. Graph the solution set, and write the solution set in set-builder notation and interval notation. Write numbers as simplified fractions or integers. \[ -11>6(x-4)+7 \] Part: $0 / 3$ Part 1 of 3 The solution set in set-builder notation is
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Solution

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Solution Steps

Step 1: Simplify the Inequality

The given inequality is:

\[ -11 > 6(x-4) + 7 \]

First, distribute the 6:

\[ -11 > 6x - 24 + 7 \]

Combine like terms:

\[ -11 > 6x - 17 \]

Step 2: Isolate the Variable

Add 17 to both sides to isolate the term with \(x\):

\[ -11 + 17 > 6x \]

Simplify:

\[ 6 > 6x \]

Step 3: Solve for \(x\)

Divide both sides by 6:

\[ 1 > x \]

or equivalently:

\[ x < 1 \]

Final Answer

The solution set in set-builder notation is \(\{ x \mid x < 1 \}\).

The solution set in interval notation is \((- \infty, 1)\).

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -2, "ymax": 2}, "commands": ["y = 1"], "latex_expressions": ["$x < 1$"]}

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