QuestionSolve the inequality $4(5 x+3) \leq 18 x+30$ . What are the possible values for $x$ ?

Studdy Solution

STEP 1

Assumptions1. The given inequality is $4(5x+3) \leq18x+30$ . We need to solve for $x$

STEP 2

First, we need to distribute the $4$ on the left side of the inequality.
$4(5x+) =20x +12$ So, the inequality becomes $20x +12 \leq18x +30$

STEP 3

Next, we need to isolate $x$ by subtracting $18x$ from both sides of the inequality.
$20x -18x +12 \leq18x -18x +30$ This simplifies to $2x +12 \leq30$

STEP 4

Then, we subtract $12$ from both sides of the inequality to isolate $2x$ .
$2x +12 -12 \leq30 -12$ This simplifies to $2x \leq18$

STEP 5

Finally, we divide both sides of the inequality by $2$ to solve for $x$ .
$\frac{2x}{2} \leq \frac{18}{2}$ This simplifies to $x \leq9$ So, the solution to the inequality $4(5x+3) \leq18x+30$ is $x \leq9$ .

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QuestionSolve the inequality $4(5 x+3) \leq 18 x+30$ . What are the possible values for $x$ ?

Studdy Solution

STEP 1

Assumptions1. The given inequality is $4(5x+3) \leq18x+30$ . We need to solve for $x$

STEP 2

First, we need to distribute the $4$ on the left side of the inequality.
$4(5x+) =20x +12$ So, the inequality becomes $20x +12 \leq18x +30$

STEP 3

Next, we need to isolate $x$ by subtracting $18x$ from both sides of the inequality.
$20x -18x +12 \leq18x -18x +30$ This simplifies to $2x +12 \leq30$

STEP 4

Then, we subtract $12$ from both sides of the inequality to isolate $2x$ .
$2x +12 -12 \leq30 -12$ This simplifies to $2x \leq18$

STEP 5

Finally, we divide both sides of the inequality by $2$ to solve for $x$ .
$\frac{2x}{2} \leq \frac{18}{2}$ This simplifies to $x \leq9$ So, the solution to the inequality $4(5x+3) \leq18x+30$ is $x \leq9$ .

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QuestionSolve the inequality 4(5x+3)≤18x+304(5 x+3) \leq 18 x+304(5x+3)≤18x+30. What are the possible values for xxx?

Studdy Solution

STEP 1

Assumptions1. The given inequality is 4(5x+3)≤18x+304(5x+3) \leq18x+304(5x+3)≤18x+30 . We need to solve for xxx

STEP 2

First, we need to distribute the 444 on the left side of the inequality.4(5x+)=20x+124(5x+) =20x +124(5x+)=20x+12So, the inequality becomes20x+12≤18x+3020x +12 \leq18x +3020x+12≤18x+30

STEP 3

Next, we need to isolate xxx by subtracting 18x18x18x from both sides of the inequality.20x−18x+12≤18x−18x+3020x -18x +12 \leq18x -18x +3020x−18x+12≤18x−18x+30This simplifies to2x+12≤302x +12 \leq302x+12≤30

STEP 4

Then, we subtract 121212 from both sides of the inequality to isolate 2x2x2x.2x+12−12≤30−122x +12 -12 \leq30 -122x+12−12≤30−12This simplifies to2x≤182x \leq182x≤18

STEP 5

Finally, we divide both sides of the inequality by 222 to solve for xxx.2x2≤182\frac{2x}{2} \leq \frac{18}{2}22x​≤218​This simplifies tox≤9x \leq9x≤9So, the solution to the inequality 4(5x+3)≤18x+304(5x+3) \leq18x+304(5x+3)≤18x+30 is x≤9x \leq9x≤9.

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QuestionSolve the inequality $4(5 x+3) \leq 18 x+30$ . What are the possible values for $x$ ?

Assumptions1. The given inequality is $4(5x+3) \leq18x+30$ . We need to solve for $x$

First, we need to distribute the $4$ on the left side of the inequality.
$4(5x+) =20x +12$ So, the inequality becomes $20x +12 \leq18x +30$

Next, we need to isolate $x$ by subtracting $18x$ from both sides of the inequality.
$20x -18x +12 \leq18x -18x +30$ This simplifies to $2x +12 \leq30$

Then, we subtract $12$ from both sides of the inequality to isolate $2x$ .
$2x +12 -12 \leq30 -12$ This simplifies to $2x \leq18$

Finally, we divide both sides of the inequality by $2$ to solve for $x$ .
$\frac{2x}{2} \leq \frac{18}{2}$ This simplifies to $x \leq9$ So, the solution to the inequality $4(5x+3) \leq18x+30$ is $x \leq9$ .