State if the statement given below is true or false.If 7y 5 =y−4 , then y=−10 .

We have the linear equation as follows, 7y 5 =y−4 .We first need to eliminate the denominator on left side of the equation. So, multiplying each side of the given equation by 5 and simplifying using the distributive property of multiplication we get, 7y 5 ×5=5(y−4) 7y=5(y−4) 7y=5(y)+5(−4) 7y=5y−20 Subtracting -5y on both sides, we get, 7y−5y=5y−5y−20 2y=−20 Now, we will divide each side by 2, 2y 2 = −20 2 y=−10 y=−10 is the solution of the given equation.Hence, the given statement is true.Hence, the correct option is 1.

State if the statement given below is true or false.If 7y 5 =y−4 , then y=−10 .

We have the linear equation as follows, 7y 5 =y−4 .We first need to eliminate the denominator on left side of the equation. So, multiplying each side of the given equation by 5 and simplifying using the distributive property of multiplication we get, 7y 5 ×5=5(y−4) 7y=5(y−4) 7y=5(y)+5(−4) 7y=5y−20 Subtracting -5y on both sides, we get, 7y−5y=5y−5y−20 2y=−20 Now, we will divide each side by 2, 2y 2 = −20 2 y=−10 y=−10 is the solution of the given equation.Hence, the given statement is true.Hence, the correct option is 1.

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State if the statement given below is true or false.

If $\frac{7 y}{5} = y - 4$ , then $y = - 10$ .

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Detailed Solution

We have the linear equation as follows,

\frac{7 y}{5} = y - 4

.
We first need to eliminate the denominator on left side of the equation. So, multiplying each side of the given equation by 5 and simplifying using the distributive property of multiplication we get,