Help-I just started Algebra II and I'm lost.
What is the solution of 10 = absolute value of 7-3x.
Please show steps so I can understand
If |7-3x| = 10
then either (7-3x) = 10 or -(7-3x) = 10
for 7-3x = 10
-3x = 3
x = -1
for -7 + 3x = 10
3x = 17
x = 17/3
so x = -1 or x = 17/3
Thank you so much
No problem! I can walk you through it step by step.
Step 1: Begin by rewriting the absolute value equation as two separate equations by considering both the positive and negative values of the absolute value expression.
Equation 1: 10 = 7 - 3x (Ignoring the absolute value)
Equation 2: 10 = -(7 - 3x) (Considering the negative value of the absolute value expression)
Step 2: Solve Equation 1 for x
First, subtract 7 from both sides of the equation:
10 - 7 = -3x
Simplify:
3 = -3x
To isolate x, divide both sides of the equation by -3:
3/-3 = -3x/-3
Simplify:
-1 = x
So, x = -1 is a solution for Equation 1.
Step 3: Solve Equation 2 for x
First, simplify the equation by distributing the negative sign:
10 = -7 + 3x
Next, add 7 to both sides of the equation:
10 + 7 = -7 + 3x + 7
Simplify:
17 = 3x
To isolate x, divide both sides of the equation by 3:
17/3 = 3x/3
Simplify (you can round if needed):
x ≈ 5.67
So, x ≈ 5.67 is a solution for Equation 2.
Step 4: Write down the solutions
The equation 10 = |7 - 3x| has two solutions:
x = -1 and x ≈ 5.67
I hope this helps! Let me know if you have any further questions.