|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
To solve the equation |a| - three-fourths = -five-eighths, we can rearrange the equation to isolate the absolute value of a:
|a| = -five-eighths + three-fourths
|a| = -five-eighths + six-eighths
|a| = one-eighth
Therefore, the absolute value of a is one-eighth or -one-eighth.
So, the correct response is: one-eighth or -one-eighth.
To solve the equation |a| − three-fourths = − five-eighths, we need to isolate the variable "a".
First, let's consider the case where a is positive: |a|.
|a| - three-fourths = -five-eighths
Since absolute value disregards the sign of a, we can rewrite |a| as a.
a - three-fourths = -five-eighths
Next, let's consider the case where a is negative: -|a|.
-|a| - three-fourths = - five-eighths
Since absolute value disregards the sign of a, we can rewrite -|a| as -a.
-a - three-fourths = -five-eighths
Now let's solve each case individually:
Case 1: a - three-fourths = -five-eighths
To isolate the variable "a", we need to get rid of the constant term (- three-fourths) on the left side of the equation. We can do this by adding three-fourths to both sides:
a - three-fourths + three-fourths = -five-eighths + three-fourths
This simplifies to:
a = -five-eighths + three-fourths
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 8:
a = (-five-eighths)*8/8 + (three-fourths)*8/8
This simplifies to:
a = -40/8 + 24/8
Adding the fractions gives:
a = -16/8
Simplifying the fraction gives:
a = -2
So, when a is positive, the solution is a = -2.
Case 2: -a - three-fourths = -five-eighths
Here, we also need to get rid of the constant term (- three-fourths) on the left side of the equation. We can do this by adding three-fourths to both sides:
-a - three-fourths + three-fourths = -five-eighths + three-fourths
This simplifies to:
-a = -five-eighths + three-fourths
Using the same steps as before, we find:
-a = -40/8 + 24/8
Adding the fractions gives:
-a = -16/8
Simplifying the fraction gives:
-a = -2
To solve for "a", we need to multiply both sides by -1:
a = (-2) *(-1)
This gives:
a = 2
Therefore, when a is negative, the solution is a = 2.
In summary, the solutions for the equation |a| - three-fourths = -five-eighths are:
When a is positive: a = -2
When a is negative: a = 2