Answer :

GinnyAnswer
To solve for [tex]\( y \)[/tex] in the equation

[tex]\[ -\frac{7}{4} y = -35, \][/tex]

we need to isolate [tex]\( y \)[/tex]. We can do this by getting rid of the fraction that is multiplying [tex]\( y \)[/tex]. Here's how to proceed step by step:

1. Identify the coefficient of [tex]\( y \)[/tex]: In the equation, the coefficient of [tex]\( y \)[/tex] is [tex]\( -\frac{7}{4} \)[/tex].

2. Reciprocal of the coefficient: To isolate [tex]\( y \)[/tex], we can multiply both sides of the equation by the reciprocal of [tex]\( -\frac{7}{4} \)[/tex]. The reciprocal of [tex]\( -\frac{7}{4} \)[/tex] is [tex]\( -\frac{4}{7} \)[/tex].

3. Multiply both sides by the reciprocal: Now, multiply both sides of the equation by [tex]\( -\frac{4}{7} \)[/tex]:

[tex]\[ \left( -\frac{4}{7} \right) \left( -\frac{7}{4} y \right) = \left( -\frac{4}{7} \right)(-35). \][/tex]

4. Simplify the left side: When you multiply [tex]\( -\frac{4}{7} \)[/tex] by [tex]\( -\frac{7}{4} \)[/tex], the [tex]\( y \)[/tex] on the left side remains because:

[tex]\[ \left( -\frac{4}{7} \right) \left( -\frac{7}{4} \right) = 1. \][/tex]

Hence,

[tex]\[ 1 \cdot y = y. \][/tex]

5. Simplify the right side: Now, simplify the right side of the equation:

[tex]\[ -35 \cdot \left( -\frac{4}{7} \right) = 20. \][/tex]

Therefore, the equation simplifies to:

[tex]\[ y = 20. \][/tex]

So, the solution is:

[tex]\[ \boxed{20}. \][/tex]

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