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a) Simplify $3(4 - 5x) - 2(5 - 6x)$ - Leaving Cert Mathematics - Question 3 - 2015
Question 3
a) Simplify $3(4 - 5x) - 2(5 - 6x)$. b) List all the values of $x$ that satisfy the inequality $2 - 3x \geq -6$, \( x \in \mathbb{N}$. c) $g(x)$ is a function ... show full transcript
Worked Solution & Example Answer:a) Simplify $3(4 - 5x) - 2(5 - 6x)$ - Leaving Cert Mathematics - Question 3 - 2015
Step 1
Step 2
b) List all the values of $x$ that satisfy the inequality $2 - 3x \geq -6$, \( x \in \mathbb{N}$
Answer
- Start with the inequality:
[ 2 - 3x \geq -6 ] - Subtract 2 from both sides:
[ -3x \geq -8 ] - Divide by -3 (remember to flip the inequality):
[ x \leq \frac{8}{3} ] - Since ( x \in \mathbb{N} ), valid values are and . Therefore, ( x \in {1, 2}$.
Step 3
c) $g(x)$ is a function and $(2 - 3x) \times g(x) = 15x^2 - 22x + 8$, for all $x \in \mathbb{R}$. Find $g(x)$.
Answer
To find , we start with the equation:
- Rearranging gives:
[ g(x) = \frac{15x^2 - 22x + 8}{2 - 3x} ] - To solve, we can factor or simplify:
- Setting up:
[ g(x) = \frac{15x^2 - 10x - 12x + 8}{2 - 3x} ] - Observe: this cancellation might give us insights into .
- Setting up:
- After performing polynomial long division or identifying patterns, we find that:
[ g(x) = -5x + 4 ]
This is our final function value.