Question Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality $18 < 4m - 15$ .
2. We need to solve for the variable $m$ .

STEP 2

First, we need to isolate the term containing the variable $m$ on one side of the inequality. To do this, we will add $15$ to both sides of the inequality to eliminate the $-15$ term on the right side.
$18 + 15 < 4m - 15 + 15$

STEP 3

Perform the addition on both sides of the inequality.
$33 < 4m$

STEP 4

Now, we need to isolate $m$ by dividing both sides of the inequality by $4$ .
$\frac{33}{4} < m$

STEP 5

Simplify the left side of the inequality to get the solution.
$m > \frac{33}{4}$

STEP 6

If desired, we can convert the improper fraction to a mixed number or a decimal to better understand the value of $m$ .
$m > 8.25$
The solution to the inequality is $m > 8.25$ .

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Question Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the inequality $18 < 4m - 15$ .
2. We need to solve for the variable $m$ .

STEP 2

First, we need to isolate the term containing the variable $m$ on one side of the inequality. To do this, we will add $15$ to both sides of the inequality to eliminate the $-15$ term on the right side.
$18 + 15 < 4m - 15 + 15$

STEP 3

Perform the addition on both sides of the inequality.
$33 < 4m$

STEP 4

Now, we need to isolate $m$ by dividing both sides of the inequality by $4$ .
$\frac{33}{4} < m$

STEP 5

Simplify the left side of the inequality to get the solution.
$m > \frac{33}{4}$

STEP 6

If desired, we can convert the improper fraction to a mixed number or a decimal to better understand the value of $m$ .
$m > 8.25$
The solution to the inequality is $m > 8.25$ .

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Question Solve the linear inequality 18<4m−1518 < 4m - 1518<4m−15 for the variable mmm.

Studdy Solution

STEP 1

Assumptions1. We are given the inequality 18<4m−1518 < 4m - 1518<4m−15.2. We need to solve for the variable mmm.

STEP 2

First, we need to isolate the term containing the variable mmm on one side of the inequality. To do this, we will add 151515 to both sides of the inequality to eliminate the −15-15−15 term on the right side.18+15<4m−15+1518 + 15 < 4m - 15 + 1518+15<4m−15+15

STEP 3

Perform the addition on both sides of the inequality.33<4m33 < 4m33<4m

STEP 4

Now, we need to isolate mmm by dividing both sides of the inequality by 444.334<m\frac{33}{4} < m433​<m

STEP 5

Simplify the left side of the inequality to get the solution.m>334m > \frac{33}{4}m>433​

STEP 6

If desired, we can convert the improper fraction to a mixed number or a decimal to better understand the value of mmm.m>8.25m > 8.25m>8.25The solution to the inequality is m>8.25m > 8.25m>8.25.

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Question Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

Assumptions
1. We are given the inequality $18 < 4m - 15$ .
2. We need to solve for the variable $m$ .

First, we need to isolate the term containing the variable $m$ on one side of the inequality. To do this, we will add $15$ to both sides of the inequality to eliminate the $-15$ term on the right side.
$18 + 15 < 4m - 15 + 15$

Perform the addition on both sides of the inequality.
$33 < 4m$

Now, we need to isolate $m$ by dividing both sides of the inequality by $4$ .
$\frac{33}{4} < m$

Simplify the left side of the inequality to get the solution.
$m > \frac{33}{4}$

If desired, we can convert the improper fraction to a mixed number or a decimal to better understand the value of $m$ .
$m > 8.25$
The solution to the inequality is $m > 8.25$ .