Solving Linear Equations Online Practice

Question

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Question
Which answer gives all the values of x
for which the inequality 3x+2≥9−4x
is true?(1 point)
Responses

x≤1
x less-than-or-equal-to 1

x=1
x equals 1

x≥1
x greater-than-or-equal-to 1

x>1

Answer 1

To solve the inequality \( 3x + 2 \geq 9 - 4x \), we can follow these steps:

1. Start by isolating \( x \) on one side of the inequality. First, add \( 4x \) to both sides: \[ 3x + 4x + 2 \geq 9 \] This simplifies to: \[ 7x + 2 \geq 9 \]

2. Next, subtract \( 2 \) from both sides: \[ 7x \geq 9 - 2 \] Which simplifies to: \[ 7x \geq 7 \]

3. Finally, divide both sides by \( 7 \): \[ x \geq 1 \]

The solution to the inequality is \( x \geq 1 \).

Therefore, the correct response is: x ≥ 1 (x greater-than-or-equal-to 1).