Math / Algebra

Question9. What is the solution of the inequality $2 x-9<7$ ? (A) $x<8$ (B) $x \leq 8$ (C) $x>8$ (D) $x \geq 8$

Studdy Solution

STEP 1

1. The inequality $2x - 9 < 7$ is a linear inequality.
2. We are solving for $x$ to find the range of values that satisfy the inequality.
3. The inequality involves basic algebraic operations, specifically addition and division.

STEP 2

1. Isolate the variable $x$ by performing algebraic operations.
2. Simplify the inequality to find the solution.
3. Compare the solution with the given options to determine the correct answer.

STEP 3

To isolate $x$ , start by adding 9 to both sides of the inequality:
$2x - 9 + 9 < 7 + 9$
This simplifies to:
$2x < 16$

STEP 4

Next, divide both sides of the inequality by 2 to solve for $x$ :
$\frac{2x}{2} < \frac{16}{2}$
This simplifies to:
$x < 8$

STEP 5

Compare the solution $x < 8$ with the given options:
(A) $x < 8$ (B) $x \leq 8$ (C) $x > 8$ (D) $x \geq 8$
The correct answer is option (A) $x < 8$ .

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Question9. What is the solution of the inequality $2 x-9<7$ ? (A) $x<8$ (B) $x \leq 8$ (C) $x>8$ (D) $x \geq 8$

Studdy Solution

STEP 1

1. The inequality $2x - 9 < 7$ is a linear inequality.
2. We are solving for $x$ to find the range of values that satisfy the inequality.
3. The inequality involves basic algebraic operations, specifically addition and division.

STEP 2

1. Isolate the variable $x$ by performing algebraic operations.
2. Simplify the inequality to find the solution.
3. Compare the solution with the given options to determine the correct answer.

STEP 3

To isolate $x$ , start by adding 9 to both sides of the inequality:
$2x - 9 + 9 < 7 + 9$
This simplifies to:
$2x < 16$

STEP 4

Next, divide both sides of the inequality by 2 to solve for $x$ :
$\frac{2x}{2} < \frac{16}{2}$
This simplifies to:
$x < 8$

STEP 5

Compare the solution $x < 8$ with the given options:
(A) $x < 8$ (B) $x \leq 8$ (C) $x > 8$ (D) $x \geq 8$
The correct answer is option (A) $x < 8$ .

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Question9. What is the solution of the inequality 2x−9<72 x-9<72x−9<7 ? (A) x<8x<8x<8 (B) x≤8x \leq 8x≤8 (C) x>8x>8x>8 (D) x≥8x \geq 8x≥8

Studdy Solution

STEP 1

1. The inequality 2x−9<7 2x - 9 < 7 2x−9<7 is a linear inequality.2. We are solving for x x x to find the range of values that satisfy the inequality.3. The inequality involves basic algebraic operations, specifically addition and division.

STEP 2

1. Isolate the variable x x x by performing algebraic operations.2. Simplify the inequality to find the solution.3. Compare the solution with the given options to determine the correct answer.

STEP 3

To isolate x x x, start by adding 9 to both sides of the inequality:2x−9+9<7+9 2x - 9 + 9 < 7 + 9 2x−9+9<7+9This simplifies to:2x<16 2x < 16 2x<16

STEP 4

Next, divide both sides of the inequality by 2 to solve for x x x:2x2<162 \frac{2x}{2} < \frac{16}{2} 22x​<216​This simplifies to:x<8 x < 8 x<8

STEP 5

Compare the solution x<8 x < 8 x<8 with the given options:(A) x<8 x < 8 x<8 (B) x≤8 x \leq 8 x≤8 (C) x>8 x > 8 x>8 (D) x≥8 x \geq 8 x≥8 The correct answer is option (A) x<8 x < 8 x<8.

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Question9. What is the solution of the inequality $2 x-9<7$ ? (A) $x<8$ (B) $x \leq 8$ (C) $x>8$ (D) $x \geq 8$

1. The inequality $2x - 9 < 7$ is a linear inequality.
2. We are solving for $x$ to find the range of values that satisfy the inequality.
3. The inequality involves basic algebraic operations, specifically addition and division.

1. Isolate the variable $x$ by performing algebraic operations.
2. Simplify the inequality to find the solution.
3. Compare the solution with the given options to determine the correct answer.

To isolate $x$ , start by adding 9 to both sides of the inequality:
$2x - 9 + 9 < 7 + 9$
This simplifies to:
$2x < 16$

Next, divide both sides of the inequality by 2 to solve for $x$ :
$\frac{2x}{2} < \frac{16}{2}$
This simplifies to:
$x < 8$

Compare the solution $x < 8$ with the given options:
(A) $x < 8$ (B) $x \leq 8$ (C) $x > 8$ (D) $x \geq 8$
The correct answer is option (A) $x < 8$ .