need help thank-you translate the verbal phrase into an inequality, then solve the inequality and graph your solution, the product of 6 and the difference of 6x and 3 is less than or equal to the product of -2 and the sum of 4 and 8x
Assistance needed.
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6(6x-3)<=-2(4+8x)
solve for x.
36x-18<=-8-16x
add 16 x to both sides, add 18 to both sides.
To translate the verbal phrase into an inequality, we need to break down the given information step by step.
Let's start with the verbal phrase:
"The product of 6 and the difference of 6x and 3 is less than or equal to the product of -2 and the sum of 4 and 8x."
Step 1: The product of 6 and the difference of 6x and 3 can be written as 6 * (6x - 3).
Step 2: The product of -2 and the sum of 4 and 8x can be written as -2 * (4 + 8x).
Now we can create the inequality:
6 * (6x - 3) <= -2 * (4 + 8x)
To solve the inequality, follow these steps:
Step 1: Distribute the multiplication on both sides of the inequality:
36x - 18 <= -8 - 16x
Step 2: Combine like terms by adding or subtracting:
36x + 16x <= -8 + 18
52x <= 10
Step 3: Divide both sides of the inequality by 52:
x <= 10/52 (or simplified, x <= 5/26)
Now, let's graph the solution on a number line:
On the number line, mark a point at 5/26 (or 0.192 rounded to three decimal places). Since the inequality is less than or equal to, include a solid dot on the marked point. Then shade the left side of the dot to represent all the values less than or equal to 5/26.
So, the solution can be graphed as x <= 5/26.
I hope this explanation helps! If you have any further questions, feel free to ask.