Math / Algebra

QuestionSolve for $x$ . $2 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>11$
Choose 1 answer: (A) $x>1$ (B) $x \geq 2$ (C) $x \leq 2$ (D) There are no solutions (E) All values of $x$ are solutions

Studdy Solution

STEP 1

1. The problem involves solving a compound inequality with two separate inequalities connected by the word "OR."
2. We need to find the values of $x$ that satisfy at least one of the inequalities.
3. The solution set is the union of the solution sets of the individual inequalities.

STEP 2

1. Solve the first inequality $2x + 3 \geq 7$ .
2. Solve the second inequality $2x + 9 > 11$ .
3. Combine the solutions using the "OR" condition.
4. Compare the combined solution with the given choices.

STEP 3

Solve the first inequality $2x + 3 \geq 7$ .
Subtract 3 from both sides:
$2x + 3 - 3 \geq 7 - 3$
Simplify:
$2x \geq 4$
Divide both sides by 2:
$x \geq 2$

STEP 4

Solve the second inequality $2x + 9 > 11$ .
Subtract 9 from both sides:
$2x + 9 - 9 > 11 - 9$
Simplify:
$2x > 2$
Divide both sides by 2:
$x > 1$

STEP 5

Combine the solutions using the "OR" condition:
The solution to the first inequality is $x \geq 2$ .
The solution to the second inequality is $x > 1$ .
Since the inequalities are connected by "OR," we take the union of the solutions.
The combined solution is $x > 1$ .

STEP 6

Compare the combined solution with the given choices:
(A) $x > 1$ - This matches our combined solution. (B) $x \geq 2$ - This is more restrictive than our solution. (C) $x \leq 2$ - This does not match our solution. (D) There are no solutions - This is incorrect. (E) All values of $x$ are solutions - This is incorrect.
The correct answer is (A) $x > 1$ .

Was this helpful?

QuestionSolve for $x$ . $2 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>11$
Choose 1 answer: (A) $x>1$ (B) $x \geq 2$ (C) $x \leq 2$ (D) There are no solutions (E) All values of $x$ are solutions

Studdy Solution

STEP 1

1. The problem involves solving a compound inequality with two separate inequalities connected by the word "OR."
2. We need to find the values of $x$ that satisfy at least one of the inequalities.
3. The solution set is the union of the solution sets of the individual inequalities.

STEP 2

1. Solve the first inequality $2x + 3 \geq 7$ .
2. Solve the second inequality $2x + 9 > 11$ .
3. Combine the solutions using the "OR" condition.
4. Compare the combined solution with the given choices.

STEP 3

Solve the first inequality $2x + 3 \geq 7$ .
Subtract 3 from both sides:
$2x + 3 - 3 \geq 7 - 3$
Simplify:
$2x \geq 4$
Divide both sides by 2:
$x \geq 2$

STEP 4

Solve the second inequality $2x + 9 > 11$ .
Subtract 9 from both sides:
$2x + 9 - 9 > 11 - 9$
Simplify:
$2x > 2$
Divide both sides by 2:
$x > 1$

STEP 5

Combine the solutions using the "OR" condition:
The solution to the first inequality is $x \geq 2$ .
The solution to the second inequality is $x > 1$ .
Since the inequalities are connected by "OR," we take the union of the solutions.
The combined solution is $x > 1$ .

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for xxx. 2x+3≥7 OR 2x+9>112 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>112x+3≥7 OR 2x+9>11Choose 1 answer: (A) x>1x>1x>1 (B) x≥2x \geq 2x≥2 (C) x≤2x \leq 2x≤2 (D) There are no solutions (E) All values of xxx are solutions

Studdy Solution

STEP 1

1. The problem involves solving a compound inequality with two separate inequalities connected by the word "OR."2. We need to find the values of x x x that satisfy at least one of the inequalities.3. The solution set is the union of the solution sets of the individual inequalities.

STEP 2

1. Solve the first inequality 2x+3≥7 2x + 3 \geq 7 2x+3≥7.2. Solve the second inequality 2x+9>11 2x + 9 > 11 2x+9>11.3. Combine the solutions using the "OR" condition.4. Compare the combined solution with the given choices.

STEP 3

Solve the first inequality 2x+3≥7 2x + 3 \geq 7 2x+3≥7.Subtract 3 from both sides:2x+3−3≥7−3 2x + 3 - 3 \geq 7 - 3 2x+3−3≥7−3Simplify:2x≥4 2x \geq 4 2x≥4Divide both sides by 2:x≥2 x \geq 2 x≥2

STEP 4

Solve the second inequality 2x+9>11 2x + 9 > 11 2x+9>11.Subtract 9 from both sides:2x+9−9>11−9 2x + 9 - 9 > 11 - 9 2x+9−9>11−9Simplify:2x>2 2x > 2 2x>2Divide both sides by 2:x>1 x > 1 x>1

STEP 5

Combine the solutions using the "OR" condition:The solution to the first inequality is x≥2 x \geq 2 x≥2.The solution to the second inequality is x>1 x > 1 x>1.Since the inequalities are connected by "OR," we take the union of the solutions.The combined solution is x>1 x > 1 x>1.

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for $x$ . $2 x+3 \geq 7 \quad \text { OR } \quad 2 x+9>11$
Choose 1 answer: (A) $x>1$ (B) $x \geq 2$ (C) $x \leq 2$ (D) There are no solutions (E) All values of $x$ are solutions

1. The problem involves solving a compound inequality with two separate inequalities connected by the word "OR."
2. We need to find the values of $x$ that satisfy at least one of the inequalities.
3. The solution set is the union of the solution sets of the individual inequalities.

1. Solve the first inequality $2x + 3 \geq 7$ .
2. Solve the second inequality $2x + 9 > 11$ .
3. Combine the solutions using the "OR" condition.
4. Compare the combined solution with the given choices.

Solve the first inequality $2x + 3 \geq 7$ .
Subtract 3 from both sides:
$2x + 3 - 3 \geq 7 - 3$
Simplify:
$2x \geq 4$
Divide both sides by 2:
$x \geq 2$

Solve the second inequality $2x + 9 > 11$ .
Subtract 9 from both sides:
$2x + 9 - 9 > 11 - 9$
Simplify:
$2x > 2$
Divide both sides by 2:
$x > 1$

Combine the solutions using the "OR" condition:
The solution to the first inequality is $x \geq 2$ .
The solution to the second inequality is $x > 1$ .
Since the inequalities are connected by "OR," we take the union of the solutions.
The combined solution is $x > 1$ .