Distribute Negative Sign: Distribute the negative sign through the parentheses. 4x - (x - 11) = 4x - x + 11Combine Like Terms: Combine like terms on the left side of the inequality. 4x - x + 11 = 3x + 11Subtract x: Subtract x from both sides to get all the x terms on one side. 3x + 11 - x <= x - 3 - xCombine Like Terms: Combine like terms on both sides. 2x + 11 <= -3Subtract 11: Subtract 11 from both sides to isolate the term with x. 2x + 11 - 11 <= -3 - 11Combine Like Terms: Combine like terms on both sides. 2x <= -14Divide by 2: Divide both sides by 2 to solve for x. 2x / 2 <= -14 / 2Simplify and Solve: Simplify both sides. x <= -7

Algebra 1

Solve advanced linear inequalities

Full solution

4 x-(x-11) \leq x-3

Distribute Negative Sign: Distribute the negative sign through the parentheses. $4x - (x - 11) = 4x - x + 11$
Combine Like Terms: Combine like terms on the left side of the inequality. $4x - x + 11 = 3x + 11$
Subtract $x$ : Subtract $x$ from both sides to get all the $x$ terms on one side. $\newline$ $3x + 11 - x \leq x - 3 - x$
Combine Like Terms: Combine like terms on both sides. $\newline$ $2x + 11 \leq -3$
Subtract $11$ : Subtract $11$ from both sides to isolate the term with $x$ . $\newline$ $2x + 11 - 11 \leq -3 - 11$
Combine Like Terms: Combine like terms on both sides. $\newline$ $2x \leq -14$
Divide by $2$ : Divide both sides by $2$ to solve for $x$ . $\frac{2x}{2} \leq \frac{-14}{2}$
Simplify and Solve: Simplify both sides. $x \leq -7$