|a| −three-fourths = −five-eighths
(1 point)
Responses
one-eighth or –one-eighth
Image with alt text: one-eighth or – Image with alt text: one-eighth
seven-eighthsor –seven-eighths
Image with alt text: seven-eighths or – Image with alt text: seven-eighths
1three-eighths or –1three-eighths
1 Image with alt text: three-eighths or –1 Image with alt text: three-eighths
no solution
no solution
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To solve the equation, subtract "three-fourths" from both sides:
|a| = -five-eighths + three-fourths
Next, find a common denominator for the fractions:
|a| = -ten-eighths + six-eighths
|a| = -four-eighths
Simplify the fraction:
|a| = -one-half
The solution is "one-half" or "-one-half".
To solve the equation |a| - three-fourths = -five-eighths, you need to isolate the absolute value term (|a|) by adding three-fourths to both sides of the equation.
When you add three-fourths to both sides, the equation becomes:
|a| = -five-eighths + three-fourths.
To simplify the right side of the equation, you need to find a common denominator for -five-eighths and three-fourths, which is 8.
Convert -five-eighths and three-fourths to have a denominator of 8:
- five-eighths = -five-eighths · 1 (in the form of 8/8) = -forty over eight = -forty-eight-eighths
three-fourths = three-fourths · 2 (2/2) = six-eighths
Now, substitute the simplified values into the equation:
|a| = -forty-eight-eighths + six-eighths
Combine the two terms on the right side of the equation:
|a| = -forty-eight minus six over eight-eighths
|-a|= -forty-two over eight-eighths
The absolute value of a number cannot be negative, so this equation has no solution, and the answer is "no solution."
To solve the equation |a| - three-fourths = -five-eighths, you can follow these steps:
1. Add three-fourths to both sides of the equation to isolate the absolute value term:
|a| = -five-eighths + three-fourths
2. Simplify the right side of the equation by finding a common denominator:
|a| = -10/8 + 6/8
|a| = -4/8
3. Simplify the absolute value term by taking the positive and negative values:
a = 4/8 or a = -4/8
4. Simplify the fractions:
a = 1/2 or a = -1/2
Therefore, the solutions to the equation are:
a = 1/2 or a = -1/2