Algebra: Solving Absolute Value Expression
We are given the equation $a - 5 = b$ and asked to find the value of the expression $|a - b| + |b - a|$.
Step 1: Determine the Value of $a - b$
Rearrange the given equation $a - 5 = b$ to find the difference $a - b$:
$a - b = 5$
Step 2: Calculate $|a - b|$
Substitute the value of $a - b$ into the first absolute value term:
$|a - b| = |5|$
The absolute value of 5 is 5:
$|a - b| = 5$
Step 3: Calculate $|b - a|$
Recognize that $b - a$ is the negative of $a - b$:
$b - a = -(a - b)$
Substitute the value of $a - b$:
$b - a = -(5) = -5$
Calculate the absolute value:
$|b - a| = |-5|$
The absolute value of -5 is 5:
$|b - a| = 5$
Step 4: Find the Total Value
Add the results from Step 2 and Step 3:
$|a - b| + |b - a| = 5 + 5$
$|a - b| + |b - a| = 10$
Similar Questions
Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
