Evaluating the given expressions and inequalities, we have;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b) = 4
[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex] 16) \: x \geq 11\frac{2}{3} [/tex]
17) k > 9
18) v > 9
20) m ≤ 16
Which method can be used to evaluate the expressions and inequalities?
The given expressions are;
[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]
Where x = 4, and y = 6, we have;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]
Therefore;
[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]
12) (8•a - 5•b) - 2•(a + b)
Where a = 3 and b = 2, we have;
(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4
Therefore;
- (8•a - 5•b) - 2•(a + b) = 4
[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]
Where a = 7, and p = 6, we have;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]
Therefore;
[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]
[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]
Where m = 5, and n = 6, we have;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]
Therefore;
[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]
[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]
Which gives;
[tex] \frac{7}{6} \times 10 \leq x [/tex]
[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]
[tex] x \geq 11\frac{2}{3} [/tex]
17) 20 < k + 11
Therefore;
k > 20 - 11 = 9
18) 6•v > 54
v > 54 ÷ 6 = 9
Therefore;
[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]
Therefore;
2 × 8 = 16 ≥ m
Which gives;
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