Question

Solve the equation and check your solutions

Answer 1

Answer:

[10.a=11]   [12.n=25÷4] [13.h=1]

Step-by-step explanation:

10.[a-9]=20

a=20-9

a=11

12.-5[2n-6]+7=-23

23-5+7=[2n-6]

25=4n   [÷4]

n=25÷4

13.[h-5]=3h-7

h-3h=5-7

-2h=-2    [÷[-2]]

h=1

sorry i could not do 11.

Answer 2

Answer:

10)  a = 29  and  a = -11

11)  No solutions

12)  n = 6  and  n = 0

13)  h = 3

Step-by-step explanation:

The absolute value of a number is its positive numerical value.

To solve an equation containing an absolute value:

1. Isolate the absolute value on one side of the equation.
2. Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation.
3. Solve both equations.

Question 10

$|a-9|=20$

$\begin{aligned}\underline{\text{Case 1}} & & \underline{\text{Case 2}}\\a-9 & = 20 & \quad \quad a - 9 & = -20\\a & = 29 & a & = -11\end{aligned}$

Check

$\implies |29-9|=|20|=20$

$\implies |-11-9|=|-20|=20$

Therefore, the solutions are:

• a = 29
• a = -11

Question 11

$\begin{aligned} |3b+b+1|+8 & =0\\\implies |4b+1|+8 & = 0\\|4b+1| &=-8\end{aligned}$

Cannot be solved as an absolute value is always positive.

Question 12

$\begin{aligned}-5|2n-6|+7 & =-23 \\\implies -5|2n-6| & = -30\\|2n-6| & = 6\end{aligned}$

$\begin{aligned}\underline{\text{Case 1}} & & \underline{\text{Case 2}}\\2n-6 & = 6 & \quad \quad 2n-6 & = -6\\2n & = 12 & 2n & = 0\\n & = 6 & n & = 0\end{aligned}$

Check

$\begin{aligned} \implies -5|2(6)-6|+7 & =-5|6|+7\\ &=-5(6)+7 \\ & =-30+7 \\ & =-23 \end{aligned}$

$\begin{aligned} \implies -5|2(0)-6|+7 & =-5|-6|+7 \\ & =-5(6)+7 \\ & =-30+7\\ & =-23 \end{aligned}$

Therefore, the solutions are:

• n = 6
• n = 0

Question 13

$|h-5|=3h-7$

$\begin{aligned}\underline{\text{Case 1}} & & \underline{\text{Case 2}}\\h-5 & = 3h-7 & \quad \quad h-5 & = -(3h-7)\\h+2 & = 3h & h-5 & = -3h+7\\2 & = 2h & h-12 & = -3h\\h & = 1 & -12 & = -4h\\ & & h & = 3\end{aligned}$

$\begin{aligned}\implies |h-5| & =3h-7\\|1-5| & = 3(1)-7\\|-4| & = 3-7\\4 & = -4\end{aligned}$

$\begin{aligned}\implies |h-5| & =3h-7\\|1-3| & = 3(3)-7\\|-2| & = 9-7\\2 & = 2\end{aligned}$

Therefore, the only valid solution is h = 3.

Learn more about absolute values here:

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