QuestionSolve the inequality $-10 \leq \frac{9 x-4}{4}<8$ and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is $-10 \leq \frac{9 x-4}{4}<8$ . We need to solve for $x$ and write the solution in interval notation.

STEP 2

We can start by multiplying the entire inequality by4 to eliminate the denominator.
$-10 \times4 \leq9x -4 <8 \times4$

STEP 3

Perform the multiplication to simplify the inequality.
$-40 \leq9x - <32$

STEP 4

Next, we add4 to all parts of the inequality to isolate $9x$ .
$-40 +4 \leq9x <32 +4$

STEP 5

Perform the addition to simplify the inequality.
$-36 \leq9x <36$

STEP 6

Finally, we divide all parts of the inequality by9 to solve for $x$ .
$\frac{-36}{9} \leq x < \frac{36}{9}$

STEP 7

Perform the division to find the solution for $x$ .
$-4 \leq x <4$

STEP 8

The solution in interval notation is $[-4,4)$ , where the square bracket indicates that -4 is included in the interval and the round bracket indicates that4 is not included.
So, the solution is $x \in [-4,4)$ .

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QuestionSolve the inequality $-10 \leq \frac{9 x-4}{4}<8$ and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is $-10 \leq \frac{9 x-4}{4}<8$ . We need to solve for $x$ and write the solution in interval notation.

STEP 2

We can start by multiplying the entire inequality by4 to eliminate the denominator.
$-10 \times4 \leq9x -4 <8 \times4$

STEP 3

Perform the multiplication to simplify the inequality.
$-40 \leq9x - <32$

STEP 4

Next, we add4 to all parts of the inequality to isolate $9x$ .
$-40 +4 \leq9x <32 +4$

STEP 5

Perform the addition to simplify the inequality.
$-36 \leq9x <36$

STEP 6

Finally, we divide all parts of the inequality by9 to solve for $x$ .
$\frac{-36}{9} \leq x < \frac{36}{9}$

STEP 7

Perform the division to find the solution for $x$ .
$-4 \leq x <4$

STEP 8

The solution in interval notation is $[-4,4)$ , where the square bracket indicates that -4 is included in the interval and the round bracket indicates that4 is not included.
So, the solution is $x \in [-4,4)$ .

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QuestionSolve the inequality −10≤9x−44<8-10 \leq \frac{9 x-4}{4}<8−10≤49x−4​<8 and express the solution in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is −10≤9x−44<8-10 \leq \frac{9 x-4}{4}<8−10≤49x−4​<8 . We need to solve for xxx and write the solution in interval notation.

STEP 2

We can start by multiplying the entire inequality by4 to eliminate the denominator.−10×4≤9x−4<8×4-10 \times4 \leq9x -4 <8 \times4−10×4≤9x−4<8×4

STEP 3

Perform the multiplication to simplify the inequality.−40≤9x−<32-40 \leq9x - <32−40≤9x−<32

STEP 4

Next, we add4 to all parts of the inequality to isolate 9x9x9x.−40+4≤9x<32+4-40 +4 \leq9x <32 +4−40+4≤9x<32+4

STEP 5

Perform the addition to simplify the inequality.−36≤9x<36-36 \leq9x <36−36≤9x<36

STEP 6

Finally, we divide all parts of the inequality by9 to solve for xxx.−369≤x<369\frac{-36}{9} \leq x < \frac{36}{9}9−36​≤x<936​

STEP 7

Perform the division to find the solution for xxx.−4≤x<4-4 \leq x <4−4≤x<4

STEP 8

The solution in interval notation is [−4,4)[-4,4)[−4,4), where the square bracket indicates that -4 is included in the interval and the round bracket indicates that4 is not included.So, the solution is x∈[−4,4)x \in [-4,4)x∈[−4,4).

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QuestionSolve the inequality $-10 \leq \frac{9 x-4}{4}<8$ and express the solution in interval notation.

Assumptions1. The inequality is $-10 \leq \frac{9 x-4}{4}<8$ . We need to solve for $x$ and write the solution in interval notation.

We can start by multiplying the entire inequality by4 to eliminate the denominator.
$-10 \times4 \leq9x -4 <8 \times4$

Perform the multiplication to simplify the inequality.
$-40 \leq9x - <32$

Next, we add4 to all parts of the inequality to isolate $9x$ .
$-40 +4 \leq9x <32 +4$

Perform the addition to simplify the inequality.
$-36 \leq9x <36$

Finally, we divide all parts of the inequality by9 to solve for $x$ .
$\frac{-36}{9} \leq x < \frac{36}{9}$

Perform the division to find the solution for $x$ .
$-4 \leq x <4$

The solution in interval notation is $[-4,4)$ , where the square bracket indicates that -4 is included in the interval and the round bracket indicates that4 is not included.
So, the solution is $x \in [-4,4)$ .