Solve $4x+3

Q: Solve $4x+3<6x+7$

To solve the inequality $4x + 3 < 6x + 7$, we need to isolate $x$ on one side of the inequality. Let's go through the steps: 1. **Subtract $4x$ from both sides**: \[ 4x + 3 - 4x -2 \] In interval notation, this solution is expressed as $(-2, \infty)$. **Explanation of Options:** - **Option 1: (-2, $\infty$)** This option correctly represents the solution to the inequality $x > -2$. Therefore, Option 1 is the correct answer. - **Option 2: (-2, +2)** This option suggests that $x$ is between -2 and 2. However, the inequality $x > -2$ does not restrict $x$ to be less than 2. Therefore, this option is incorrect. - **Option 3: (-2, 0)** This option suggests that $x$ is between -2 and 0. However, the inequality $x > -2$ allows $x$ to be any value greater than -2, not just up to 0. Therefore, this option is incorrect. - **Option 4: (2, $\infty$)** This option suggests that $x$ is greater than 2. However, the inequality $x > -2$ allows $x$ to be any value greater than -2, not just values greater than 2. Therefore, this option is incorrect. In conclusion, Option 1 $(-2, \infty)$ is the correct answer as it accurately represents the solution to the inequality $4x + 3 < 6x + 7$.

Question

Solve $4x+3<6x+7$

Accepted Answer

To solve the inequality $4x + 3 < 6x + 7$, we need to isolate $x$ on one side of the inequality. Let's go through the steps: 1. **Subtract $4x$ from both sides**: $$ 4x + 3 - 4x < 6x + 7 - 4x $$ This simplifies to: $$ 3 < 2x + 7 $$ 2. **Subtract 7 from both sides**: $$ 3 - 7 < 2x + 7 - 7 $$ This simplifies to: $$ -4 < 2x $$ 3. **Divide both sides by 2**: $$ \frac{-4}{2} < \frac{2x}{2} $$ This simplifies to: $$ -2 < x $$ This inequality can be rewritten as: $$ x > -2 $$ In interval notation, this solution is expressed as $(-2, \infty)$. **Explanation of Options:** - **Option 1: (-2, $\infty$)** This option correctly represents the solution to the inequality $x > -2$. Therefore, Option 1 is the correct answer. - **Option 2: (-2, +2)** This option suggests that $x$ is between -2 and 2. However, the inequality $x > -2$ does not restrict $x$ to be less than 2. Therefore, this option is incorrect. - **Option 3: (-2, 0)** This option suggests that $x$ is between -2 and 0. However, the inequality $x > -2$ allows $x$ to be any value greater than -2, not just up to 0. Therefore, this option is incorrect. - **Option 4: (2, $\infty$)** This option suggests that $x$ is greater than 2. However, the inequality $x > -2$ allows $x$ to be any value greater than -2, not just values greater than 2. Therefore, this option is incorrect. In conclusion, Option 1 $(-2, \infty)$ is the correct answer as it accurately represents the solution to the inequality $4x + 3 < 6x + 7$.