a) The solution for the equation 2x + 16 = 5x + 4 is x=4.
b) The solution for the equation 3x − 5 = 2x + 14 is x=19.
c) The solution for the equation 5x − 5 = x + 15 is x=5.
<u>Step-by-step explanation:</u>
<u>a) The given equation is 2x + 16 = 5x + 4 </u>
- From the above equation, it can be found that the equation consists of x terms and constant terms.
- Therefore, bring all the x terms on one side and the constant terms on other side of the equation.
- This gives the simplified form of the equation to solve for x value.
⇒ 16-4 = 5x-2x
⇒ 12 = 3x
⇒ x = 12/3
⇒ x = 4
The solution for the given equation is x=4.
<u>To check, substitute x=4 in the equation :</u>
2(4) + 16 = 5(4) + 4
8+16 = 20+4
24 = 24
Therefore, the solution x=4 satisfies the equation 2x + 16 = 5x + 4
Similarly,
<u>b) The given equation is 3x − 5 = 2x + 14</u>
⇒ 3x-2x = 14+5
⇒ x = 19
The solution for the given equation is x=19.
<u>To check, substitute x=19 in the equation :</u>
3(19) - 5 = 2(19) + 14
57-16 = 38+14
52 = 52
Therefore, the solution x=19 satisfies the equation 3x − 5 = 2x + 14
Similarly,
<u>c) The given equation is 5x − 5 = x + 15</u>
⇒ 5x-x = 15+5
⇒ 4x = 20
⇒ x = 20/4
⇒ x = 5
The solution for the given equation is x=5.
<u>To check, substitute x=5 in the equation :</u>
5(5) - 5 = 5 + 15
25-5 = 20
20 = 20
Therefore, the solution x=5 satisfies the equation 5x − 5 = x + 15
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