Were doing Absolute value so the brackets you see are ment to be for absoulte value.
1/3[4p-11]=p+4
I know that the first answer is 1 but when your doing absolute value you have to have two solutions. so would the other solution be -23/7?
Nicole. I deleted my answer.
To solve the equation 1/3[4p - 11] = p + 4, where the brackets represent absolute value, we'll follow these steps:
Step 1: Identify the absolute value expression.
In the given equation, the absolute value expression is 4p - 11.
Step 2: Remove the absolute value brackets.
Since the absolute value expression is isolated on one side of the equation, we can remove the brackets and rewrite the equation:
1/3 * |4p - 11| = p + 4.
Step 3: Set up two equations.
To handle the absolute value, we'll set up two separate equations: one with the positive expression inside the absolute value and one with the negative expression.
1) 1/3 * (4p - 11) = p + 4 (Positive expression)
2) 1/3 * (-(4p - 11)) = p + 4 (Negative expression)
Step 4: Solve the equations separately.
Solve each equation separately to find the values of p.
For Equation 1:
Distribute 1/3 to (4p - 11):
4/3p - 11/3 = p + 4
Move all terms with p to the left side and constants to the right side:
4/3p - p = 4 + 11/3
Combine like terms:
(-1/3)p = 12/3 + 11/3
(-1/3)p = 23/3
Multiply both sides by -3 to isolate p:
(-1/3)(-3)p = (23/3)(-3)
p = -69/3
p = -23
For Equation 2:
Distribute 1/3 to (-(4p - 11)):
1/3 * (-4p + 11) = p + 4
Move all terms with p to the left side and constants to the right side:
-4/3p + 11/3 = p + 4
Combine like terms:
(-4/3)p - p = 4 + 11/3
Multiply both sides by -3 to isolate p:
(-4/3)(-3)p = (4 + 11/3)(-3)
p = (4 + 11/3)(-3)
p = -63/3
p = -21
Step 5: Check the solutions.
Substitute the values of -23 and -21 into the original equation and check if they satisfy the equation.