17-6x≥ 4x-10
The correct answer and explanation is:
To solve the inequality 17−6x≥4x−1017 – 6x \geq 4x – 10, follow these steps:
Step 1: Move all terms involving xx to one side and constants to the other side.
Start by adding 6x6x to both sides to eliminate the −6x-6x on the left side: 17≥4x−10+6×17 \geq 4x – 10 + 6x
Simplify the equation: 17≥10x−1017 \geq 10x – 10
Step 2: Move the constants to the other side.
Now, add 10 to both sides to get rid of the −10-10 on the right: 17+10≥10×17 + 10 \geq 10x
Simplify: 27≥10×27 \geq 10x
Step 3: Solve for xx.
Now, divide both sides of the inequality by 10 to isolate xx: 2710≥x\frac{27}{10} \geq x
This simplifies to: x≤2710x \leq \frac{27}{10}
Or equivalently: x≤2.7x \leq 2.7
Conclusion:
The solution to the inequality is x≤2.7x \leq 2.7, meaning that any value of xx less than or equal to 2.7 satisfies the inequality.
Explanation:
To solve inequalities like this, the goal is to isolate the variable on one side of the inequality. This involves using the same principles as solving equations, such as adding, subtracting, multiplying, and dividing both sides by the same number. However, keep in mind that if you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. Since we did not multiply or divide by a negative number in this case, the inequality sign remains as “≥”. This approach allows us to determine the possible values for xx.