Problem 87
Question
Will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$ 2(x-3)-17=13-3(x+2) $$ is the resulting statement true or false?
Step-by-Step Solution
Verified Answer
The resulting statement is true.
1Step 1: Substitute for \(x\)
Begin by substituting the value \(x = 6\) into the equation. It becomes: \(2(6-3)-17=13-3(6+2)\)
2Step 2: Simplify the equation
Next, do the arithmetic within the parenthesis first (according to order of operations), then follow through with the multiplication and subtraction: So the equation simplifies to: \[2(3) - 17 = 13 -3(8)\] \[6 -17 = 13 - 24\] \[-11 = -11\]
3Step 3: Compare both sides
Finally, examine the simplified statement. Both sides of the equation equal to \(-11\), which means the original statement is true when \(x = 6\).
Other exercises in this chapter
Problem 87
In Exercises 59–94, solve each absolute value inequality. $$ 5>|4-x| $$
View solution Problem 87
Solve equation by the method of your choice. $$ 3 x^{2}=60 $$
View solution Problem 87
Find all values of \(x\) satisfying the given conditions.. $$y=x+\sqrt{x+5} \text { and } y=7$$
View solution Problem 87
Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{3(x+3)}{5}=2 x+6\) and \(y\) satisfying \(-2 y-10=5 y+18\).
View solution