Which situation can be represented by 3x + 2 = 8x – 13?
Thirteen less than three times a number is the same as eight times the number, x, increased by 2. What is the value of x?
Three times a number decreased by 2 is the same as 8 times the number increased by 13. What is the value of x?
A square with a side length of x is dilated. Patrice described the length of the side of the new square as 2 units more than 3 times the original length. Kelvin described the length as 13 units more than 8 times the original length. What is the original length?
Kenny and Jacob were given congruent rectangles with widths of x units. The length of Kenny’s rectangle was 3 times the width increased by 2. The length of Jacob’s rectangle was 13 units less than 8 times the width. What is the width of their rectangles, x?
I will translate your first English statement into Math.
"Thirteen less than three times a number is the same as eight times the number, x, increased by 2. What is the value of x?"
3x - 13 = 8x - 2
Now do the same with the others and see which one matches your given equation.
The situation represented by the equation 3x + 2 = 8x - 13 is: "Thirteen less than three times a number is the same as eight times the number, x, increased by 2."
To solve for x, we can follow these steps:
Step 1: Group the x terms on one side of the equation and the constant terms on the other side.
3x - 8x = -13 - 2
Step 2: Simplify the equation.
-5x = -15
Step 3: Divide both sides of the equation by -5 to isolate x.
x = -15 / -5
Step 4: Simplify the expression.
x = 3
Therefore, the value of x is 3.
The situation represented by the equation 3x + 2 = 8x - 13 is "Thirteen less than three times a number is the same as eight times the number, x, increased by 2."
To find the value of x, we need to solve the equation.
Step 1: Begin by simplifying the equation by combining like terms.
3x + 2 = 8x - 13
Subtracting 3x from both sides:
2 = 5x - 13
Step 2: Next, isolate the variable term by moving constants to the other side of the equation.
Adding 13 to both sides:
15 = 5x
Step 3: Finally, solve for x by dividing both sides of the equation by 5.
x = 15/5
x = 3
Therefore, the value of x is 3.
In the second situation "Three times a number decreased by 2 is the same as 8 times the number increased by 13," the process would be the same. We would solve the equation 3x - 2 = 8x + 13 using the steps outlined above to find the value of x.
For the third and fourth situations involving squares and rectangles, the original length or width can be found by setting up and solving equations similar to the first two examples. The given information can be used to create an equation, and then the equation can be solved to find the desired value of x.