Given: \( 4-\angle x<16 \) where \( x \in \AA \) 2.1.1 Solve the inequality. 2.12 Hence, represent your answer to QUESTION 2.1.1 on a number line. Solve simultaneously for \( x \) and \( y \) : \[ -2 x-y=10 \text { and } 3 x-4 y=-4 \] Solve for \( x \) : \( 2.3 .1 \quad \frac{x(x-5)}{6}-1=0 \) \( 232 \quad e=\sqrt{a+2 x} \) Tabelo is currently four times as old as his daughter, Linda. Six years from now, Tahelo will be throc times as old as Linda. Colculate Linda'r age currently.
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First, let's tackle the inequality \( 4 - \angle x < 16 \): 1. Rearranging gives \( -\angle x < 12 \). 2. Thus, \( \angle x > -12 \). Now, regarding the graphical representation, you would draw a number line, placing an open circle on -12 and shading everything to the right, indicating all values of \( \angle x \) that satisfy the inequality. Next, solving the simultaneous equations: 1. From \( -2x - y = 10 \), we get \( y = -2x - 10 \). 2. Substituting into \( 3x - 4y = -4 \) gives: \[ 3x - 4(-2x - 10) = -4 \implies 3x + 8x + 40 = -4 \implies 11x = -44 \implies x = -4 \] 3. Plugging back to find \( y \): \[ y = -2(-4) - 10 = 8 - 10 = -2, \] So, \( (x, y) = (-4, -2) \). For Linda's age problem, let's define: - Let \( L \) be Linda's current age. - Then, Tahelo's current age is \( 4L \). In six years: - Tahelo's age: \( 4L + 6 \) - Linda's age: \( L + 6 \) From the problem, we have: \[ 4L + 6 = 3(L + 6). \] Solving gives: \[ 4L + 6 = 3L + 18 \implies L = 12. \] Thus, Linda's current age is 12.
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