Solve for j. -2(j - 16) + 13 > 15 ______

Distribute and Simplify: Distribute -2 across the parentheses in the inequality -2(j - 16) + 13 > 15. -2 * j + -2 * (-16) + 13 > 15 -2j + 32 + 13 > 15Combine Like Terms: Combine like terms on the left side of the inequality. -2j + 32 + 13 = -2j + 45 So, the inequality now is -2j + 45 > 15.Isolate Variable: Subtract 45 from both sides of the inequality to isolate the term with the variable j. -2j + 45 - 45 > 15 - 45 -2j > -30Divide and Reverse Inequality: Divide both sides of the inequality by -2 to solve for j. Remember to reverse the inequality sign because we are dividing by a negative number. -2j / -2 15 -2(-2) + 13 > 15 4 + 13 > 15 17 > 15 Since 17 is greater than 15, the inequality holds true for j < 15.

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Algebra 1

Solve advanced linear inequalities

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Q. Solve for

j

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-2(j - 16) + 13 > 15

Distribute and Simplify: Distribute $-2$ across the parentheses in the inequality -2(j - 16) + 13 > 15.-2 \times j + -2 \times (-16) + 13 > 15-2j + 32 + 13 > 15
Combine Like Terms: Combine like terms on the left side of the inequality. $\newline$ $-2j + 32 + 13 = -2j + 45$ $\newline$ So, the inequality now is -2j + 45 > 15.
Isolate Variable: Subtract $45$ from both sides of the inequality to isolate the term with the variable $j$ . $\newline$ -2j + 45 - 45 > 15 - 45 $\newline$ -2j > -30
Divide and Reverse Inequality: Divide both sides of the inequality by $-2$ to solve for $j$ . Remember to reverse the inequality sign because we are dividing by a negative number. $\newline$ -2j / -2 < -30 / -2 $\newline$ j < 15
Check Solution: Check the solution by substituting the value of $j$ back into the original inequality to see if it makes the inequality true. $\newline$ Let's choose a value less than $15$ , say $j = 14$ , and substitute it back into the original inequality: $\newline$ -2(14 - 16) + 13 > 15 $\newline$ -2(-2) + 13 > 15 $\newline$ 4 + 13 > 15 $\newline$ 17 > 15 $\newline$ Since $17$ is greater than $15$ , the inequality holds true for j < 15.