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Let’s check out your problem:
Solve the equation. Check your solution
\newline
19
=
2
−
(
z
+
5
)
19=2-(z+5)
19
=
2
−
(
z
+
5
)
\newline
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Math Problems
Calculus
Find indefinite integrals using the substitution and by parts
Full solution
Q.
Solve the equation. Check your solution
\newline
19
=
2
−
(
z
+
5
)
19=2-(z+5)
19
=
2
−
(
z
+
5
)
\newline
Rewrite Equation:
Rewrite the equation to isolate the variable
z
z
z
on one side.
\newline
19
=
2
−
(
z
+
5
)
19 = 2 - (z + 5)
19
=
2
−
(
z
+
5
)
Move Terms Left:
Move the term
(
z
+
5
)
(z + 5)
(
z
+
5
)
to the left side by adding
(
z
+
5
)
(z + 5)
(
z
+
5
)
to both sides of the equation.
\newline
19
+
(
z
+
5
)
=
2
19 + (z + 5) = 2
19
+
(
z
+
5
)
=
2
Combine Like Terms:
Combine like terms on the left side.
19
+
z
+
5
=
2
19 + z + 5 = 2
19
+
z
+
5
=
2
Simplify Left Side:
Simplify the left side by adding the numbers.
24
+
z
=
2
24 + z = 2
24
+
z
=
2
Subtract
24
24
24
:
Subtract
24
24
24
from both sides to isolate
z
z
z
.
\newline
24
+
z
−
24
=
2
−
24
24 + z - 24 = 2 - 24
24
+
z
−
24
=
2
−
24
Simplify Solution:
Simplify both sides.
\newline
z
=
−
22
z = -22
z
=
−
22
Check Solution:
Check the solution by substituting
z
=
−
22
z = -22
z
=
−
22
back into the original equation.
19
=
2
−
(
(
−
22
)
+
5
)
19 = 2 - ((-22) + 5)
19
=
2
−
((
−
22
)
+
5
)
Simplify Right Side:
Simplify the right side of the equation.
19
=
2
−
(
−
22
+
5
)
19 = 2 - (-22 + 5)
19
=
2
−
(
−
22
+
5
)
Combine Numbers:
Combine the numbers inside the parentheses.
\newline
19
=
2
−
(
−
17
)
19 = 2 - (-17)
19
=
2
−
(
−
17
)
Simplify Right Side:
Subtracting a negative is the same as adding the positive equivalent.
\newline
19
=
2
+
17
19 = 2 + 17
19
=
2
+
17
Simplify Right Side:
Subtracting a negative is the same as adding the positive equivalent.
\newline
19
=
2
+
17
19 = 2 + 17
19
=
2
+
17
Simplify the right side by adding the numbers.
\newline
19
=
19
19 = 19
19
=
19
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