Solve for w: 331 = 4.9(-4w+9) + 7
Understand the Problem
The question asks to solve the given equation for the variable 'w'. The solution should be expressed as an exact integer or fraction, and decimals should not be used. We will simplify the equation and isolate 'w'.
Answer
$w = -\frac{2799}{196}$
Answer for screen readers
$w = -\frac{2799}{196}$
Steps to Solve
- Distribute 4.9 into the parentheses
We need to multiply $4.9$ by both terms inside the parentheses: $-4w$ and $9$. $4.9 \cdot (-4w) = -19.6w$ $4.9 \cdot 9 = 44.1$ So the equation becomes: $331 = -19.6w + 44.1 + 7$
- Combine constant terms on the right side of the equation
Combine the constants $44.1$ and $7$: $44.1 + 7 = 51.1$ The equation is now: $331 = -19.6w + 51.1$
- Isolate the term with $w$
Subtract $51.1$ from both sides of the equation to isolate the term with $w$: $331 - 51.1 = -19.6w$ $279.9 = -19.6w$
- Solve for $w$
Divide both sides of the equation by $-19.6$ to solve for $w$: $w = \frac{279.9}{-19.6}$ $w = - \frac{2799}{196}$
- Simplify the fraction if possible
We can see that we need to multiply everything by $10$ to get rid of any decimals. Then, we check the value of $w$ to see if we can simplify. The fraction $-\frac{2799}{196}$ cannot be simplified.
$w = -\frac{2799}{196}$
More Information
The solution to the equation $331 = 4.9(-4w+9) + 7$ is $w = -\frac{2799}{196}$. This is an exact fraction as requested.
Tips
A common mistake would be incorrectly distributing the $4.9$ or making an arithmetic error when combining the constant terms. Another common mistake could be incorrectly dividing the numbers, paying special attention to signs. Furthermore, people may have trouble when there are decimals. Multiplying by 10 to remove the decimals is an important first step.
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