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Let’s check out your problem:
If
2
+
7
z
=
−
z
−
4
2+7z=-z-4
2
+
7
z
=
−
z
−
4
, what is the value of
z
z
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
=
−
1
z=-1
z
=
−
1
\newline
(B)
z
=
−
3
4
z=-\frac{3}{4}
z
=
−
4
3
\newline
(C)
z
=
−
1
3
z=-\frac{1}{3}
z
=
−
3
1
\newline
(D)
z
=
−
1
4
z=-\frac{1}{4}
z
=
−
4
1
View step-by-step help
Home
Math Problems
Algebra 2
Evaluate variable expressions involving rational numbers
Full solution
Q.
If
2
+
7
z
=
−
z
−
4
2+7z=-z-4
2
+
7
z
=
−
z
−
4
, what is the value of
z
z
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
=
−
1
z=-1
z
=
−
1
\newline
(B)
z
=
−
3
4
z=-\frac{3}{4}
z
=
−
4
3
\newline
(C)
z
=
−
1
3
z=-\frac{1}{3}
z
=
−
3
1
\newline
(D)
z
=
−
1
4
z=-\frac{1}{4}
z
=
−
4
1
Write Equation:
Write down the equation.
\newline
We have the equation
2
+
7
z
=
−
z
−
4
2 + 7z = -z - 4
2
+
7
z
=
−
z
−
4
.
Combine Z Terms:
Add
z
z
z
to both sides to get all the
z
z
z
terms on one side.
\newline
2
+
7
z
+
z
=
−
z
−
4
+
z
2 + 7z + z = -z - 4 + z
2
+
7
z
+
z
=
−
z
−
4
+
z
\newline
This simplifies to:
\newline
2
+
8
z
=
−
4
2 + 8z = -4
2
+
8
z
=
−
4
Isolate Z Term:
Subtract
2
2
2
from both sides to isolate the term with
z
z
z
.
\newline
2
+
8
z
−
2
=
−
4
−
2
2 + 8z - 2 = -4 - 2
2
+
8
z
−
2
=
−
4
−
2
\newline
This simplifies to:
\newline
8
z
=
−
6
8z = -6
8
z
=
−
6
Solve for Z:
Divide both sides by
8
8
8
to solve for
z
z
z
.
\newline
8
z
8
=
−
6
8
\frac{8z}{8} = \frac{-6}{8}
8
8
z
=
8
−
6
\newline
This simplifies to:
\newline
z
=
−
6
8
z = \frac{-6}{8}
z
=
8
−
6
Simplify Fraction:
Simplify the
fraction
−
6
8
-\frac{6}{8}
−
8
6
.
−
6
8
-\frac{6}{8}
−
8
6
can be reduced by dividing both the numerator and the denominator by
2
2
2
.
z
=
−
6
/
2
8
/
2
z = \frac{-6 / 2}{8 / 2}
z
=
8/2
−
6/2
z
=
−
3
4
z = -\frac{3}{4}
z
=
−
4
3
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\newline
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\newline
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