Questions: Which of the following is equivalent to 7x + 5 < -2(4x - 3)? x > 11 -x < 1 15x < -11 15x < 1

Transcript text: Which of the following is equivalent to $7 x+5<-2(4 x-3)$ ? $x>11$ $-x<1$ $15 x<-11$ $15 x<1$

Solution

Solution Steps

To solve the inequality $7x + 5 < -2(4x - 3)$, we need to first distribute the $-2$ on the right side of the inequality. Then, we will combine like terms and isolate $x$ to find the solution.

Step 1: Distributing and Rearranging the Inequality

We start with the inequality: \[ 7x + 5 < -2(4x - 3) \] Distributing $-2$ on the right side gives: \[ 7x + 5 < -8x + 6 \]

Step 2: Combining Like Terms

Next, we rearrange the inequality by adding $8x$ to both sides: \[ 7x + 8x + 5 < 6 \] This simplifies to: \[ 15x + 5 < 6 \]

Step 3: Isolating $x$

Now, we subtract $5$ from both sides: \[ 15x < 1 \] Dividing both sides by $15$ yields: \[ x < \frac{1}{15} \]

Final Answer

The solution to the inequality is: \[ \boxed{x < \frac{1}{15}} \]

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