Respuesta :
Answer:
Option A is correct.
The first step in solving the inequality is:
to distribute -4 to get [tex]-8x + 4> 5-3x[/tex]
Step-by-step explanation:
The distributive property says that:
[tex]a\cdot(b+c) =a\cdot b + a\cdot c[/tex]
Given the inequality:
[tex]-4(2x-1)> 5-3x[/tex]
Apply the distributive property we have;
[tex]-4 \cdot (2x) -4\cdot (-1)> 5-3x[/tex]
Simplify:
[tex]-8x + 4> 5-3x[/tex]
Therefore, the first step in solving the inequality is:
to distribute -4 to get [tex]-8x + 4> 5-3x[/tex]
Distribute –4 to get –8x + 4 > 5 – 3x.
Further explanation
The inequality –4(2x – 1) > 5 – 3x.
We will solve the problem of inequality of one variable. Here are the steps:
Step-1: Distribute –4 to get –8x + 4 > 5 – 3x.
–4(2x – 1) > 5 – 3x
-4(2x) + (-4)(-1) > 5 – 3x
-8x + 4 > 5 – 3x
Therefore, a correct first step in solving the inequality: Distribute –4 to get –8x + 4 > 5 – 3x.
Step-2: Subtract 4 from both sides of the inequality
-8x + 4 - 4 > 5 - 4 – 3x
-8x > 1 – 3x
Step-3: Add 3x from both sides of the inequality
-8x + 3x > 1 – 3x + 3x
-5x > 1
Step-4: Divide -5 from both sides of the inequality
[tex]\boxed{ \ \frac{-5x}{-5} > \frac{1}{-5} \ }[/tex]
Thus, the solution is [tex]\boxed{\boxed{ \ x < -\frac{1}{5} \ }}[/tex]
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Notes:
- The Distributive Property: [tex]\boxed{ \ A(B + C) = A \cdot B + A \cdot C \ }[/tex] or [tex]\boxed{ \ A(B - C) = A \cdot B - A \cdot C \ }[/tex]
- If inequality is multiplied or divided by a negative number, then the sign of the inequality changes.
Learn more
- Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38? https://brainly.com/question/1626676
- Which is the graph of 2x – 4y > 6 https://brainly.com/question/4408289#
- Which table represents a linear function https://brainly.com/question/10570936
Keywords: a correct first step, in solving the inequality, one variable, distribute, add, subtract, divide, multiply, sign, minus, negative, solution, distributive property
