Question

Give the property that justifies each step.

Answer 1

Please check the explanation below.

Explanation:

Some of the properties are defined as:

• Distributive property

a(b+c) = ab+ac

For example,

suppose a=1, b=2, c=3

1(2+3) = 1(2) + 1(3)

5 = 2+3 = 5

• Subtraction property of Equality

if (a=b), then a-c = b-c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a-c = b-c ⇒ 1-3 = 1 - 3 ⇒ -2 = -2

• Addition property of Equality

if (a=b), then a+c = b+c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a+c = b+c ⇒ 1+3 = 1+3 ⇒ 4 = 4

• Multiplicative property of Equality

if (a=b), then a×c = b×c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a×c = b×c ⇒ 1×3 = 1 × 3 ⇒ 3 = 3

• Division property of Equality

if (a=b), then a÷c = b÷c

For example,

suppose a=1, b=1, c=3

if a = b ⇒ 1 = 1

then a÷c = b÷c ⇒ 1÷3 = 1 ÷ 3 ⇒ 1/3 = 1/3

Let's solve the given equation using the above properties.

5(x+10) = 20 Given

5x+50 = 20 1) Distriburive property ∵ a(b+c) = ab+ac

5x = -30 2) Subtraction property of Equality ∵ if (a=b), then a-c = b-c

x = -6 3) Division property of Equality ∵ if (a=b), then a÷c = b÷c