QuestionSolve the inequality: $-5(x-6) \leq 3(x+2)$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is $-5(x-6) \leq3(x+)$ . We need to solve the inequality for $x$

STEP 2

First, distribute the $-5$ on the left side of the inequality and the $$ on the right side of the inequality.
-5x +30 \leqx +6

STEP 3

Now, we want to isolate $x$ on one side of the inequality. Let's start by subtracting $3x$ from both sides of the inequality.
$-5x -3x +30 \leq6$

STEP 4

implify the left side of the inequality.
$-8x +30 \leq6$

STEP 5

Next, subtract $30$ from both sides of the inequality to isolate the $x$ term on the left side.
$-8x \leq -30$

STEP 6

implify the right side of the inequality.
$-8x \leq -24$

STEP 7

Finally, divide both sides of the inequality by $-$ to solve for $x$ . Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.
$x \geq -24/-$

STEP 8

implify the right side of the inequality.
$x \geq3$ So, the solution to the inequality $-5(x-6) \leq3(x+2)$ is $x \geq3$ .

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QuestionSolve the inequality: $-5(x-6) \leq 3(x+2)$ .

Studdy Solution

STEP 1

Assumptions1. The inequality is $-5(x-6) \leq3(x+)$ . We need to solve the inequality for $x$

STEP 2

First, distribute the $-5$ on the left side of the inequality and the $$ on the right side of the inequality.
-5x +30 \leqx +6

STEP 3

Now, we want to isolate $x$ on one side of the inequality. Let's start by subtracting $3x$ from both sides of the inequality.
$-5x -3x +30 \leq6$

STEP 4

implify the left side of the inequality.
$-8x +30 \leq6$

STEP 5

Next, subtract $30$ from both sides of the inequality to isolate the $x$ term on the left side.
$-8x \leq -30$

STEP 6

implify the right side of the inequality.
$-8x \leq -24$

STEP 7

Finally, divide both sides of the inequality by $-$ to solve for $x$ . Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.
$x \geq -24/-$

STEP 8

implify the right side of the inequality.
$x \geq3$ So, the solution to the inequality $-5(x-6) \leq3(x+2)$ is $x \geq3$ .

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QuestionSolve the inequality: −5(x−6)≤3(x+2)-5(x-6) \leq 3(x+2)−5(x−6)≤3(x+2).

Studdy Solution

STEP 1

Assumptions1. The inequality is −5(x−6)≤3(x+)-5(x-6) \leq3(x+)−5(x−6)≤3(x+). We need to solve the inequality for xxx

STEP 2

First, distribute the −5-5−5 on the left side of the inequality and the $$ on the right side of the inequality.-5x +30 \leqx +6

STEP 3

Now, we want to isolate xxx on one side of the inequality. Let's start by subtracting 3x3x3x from both sides of the inequality.−5x−3x+30≤6-5x -3x +30 \leq6−5x−3x+30≤6

STEP 4

implify the left side of the inequality.−8x+30≤6-8x +30 \leq6−8x+30≤6

STEP 5

Next, subtract 303030 from both sides of the inequality to isolate the xxx term on the left side.−8x≤−30-8x \leq -30−8x≤−30

STEP 6

implify the right side of the inequality.−8x≤−24-8x \leq -24−8x≤−24

STEP 7

Finally, divide both sides of the inequality by −-− to solve for xxx. Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.x≥−24/−x \geq -24/-x≥−24/−

STEP 8

implify the right side of the inequality.x≥3x \geq3x≥3So, the solution to the inequality −5(x−6)≤3(x+2)-5(x-6) \leq3(x+2)−5(x−6)≤3(x+2) is x≥3x \geq3x≥3.

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QuestionSolve the inequality: $-5(x-6) \leq 3(x+2)$ .

Assumptions1. The inequality is $-5(x-6) \leq3(x+)$ . We need to solve the inequality for $x$

First, distribute the $-5$ on the left side of the inequality and the $$ on the right side of the inequality.
-5x +30 \leqx +6

Now, we want to isolate $x$ on one side of the inequality. Let's start by subtracting $3x$ from both sides of the inequality.
$-5x -3x +30 \leq6$

implify the left side of the inequality.
$-8x +30 \leq6$

Next, subtract $30$ from both sides of the inequality to isolate the $x$ term on the left side.
$-8x \leq -30$

implify the right side of the inequality.
$-8x \leq -24$

Finally, divide both sides of the inequality by $-$ to solve for $x$ . Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.
$x \geq -24/-$

implify the right side of the inequality.
$x \geq3$ So, the solution to the inequality $-5(x-6) \leq3(x+2)$ is $x \geq3$ .