Question

1.1 Solve the following equations by isolating the variable:
(a) a + 24 = 24
(b) 8 - 2z = 5 - 5z
14x - 12
(c)
43
2
(d) 8d - 16 = 48
(e) 7y - 9 = 4y - 6
()
77
7
7
= 48y - 26y - 55​

Answer 1

(a) a+24=24

=a=24-24

=a=0

(b) 8-2z= 5-5z

-2z+5z=5-8

3z= -3

z=-3/3

z= -1

Answer 2

For the first equation

The equation is

a + 24 = 24 ........(1)

now we add -24 both side then we get

a +24 -24 = 24-24,

a +0 = 0

a= 0.

For the second equation

The equation is

8 - 2z = 5 - 5z..........(2)

Now we add -8 both side

8 -2z -8 = 5-5z-8

-2z = -5z -3

now we add 5z both side

-2z + 5z = -5z -3 +5z

3z= -3

now we divide both side by 3

z=-1.

For the third equation

The equation is

$\frac{14x -12}{2} = 43$............ (3)

Now we multiply by 2 in both side we get

2* $\frac{14x -12}{2} = 43$ *2

14x-12= 86,

now we add 12 in both side we get

14x-12 +12= 86 +12

14x = 98

now  we divide both side by 7 we get\

x = 7.

For the forth equation

The equation is

8d - 16 = 48........(4)

Now we add 16 in both side

8d -16 +16 =48+16

8d =64

now we divide by 8 into both side

d = 8.

For the fifth equation

The equation is  7y - 9 = 4y - 6...........(5)

Now we add -4y in both side we get

7y - 9-4y = 4y -6-4y

3y -9 = -6

Now we add 9 in both side

3y - 9 +9 = -6+9

3y = 3

Now divide by 3 in both side

y=1.

For the sixth equation

The equation is

$\frac{77}{7}$ = 48y -26y-55.........(6)

Now we multiple by 7 both side we get

77 = 336y - 182y -385

77 =154y-385

Now we add 385 both side

77+385 =154y -385+385

462= 154y

now we divide by 154 both side we get

y=3

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