Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(11x-15=5\)
2. \(11x-15=-8\)
3. \(x+8=11\)
4. \(-4x-9=-7\)
5. \(-8x+3=14\)
6. \(-3x-15=11\)
7. \(-13x-1=-5\)
8. \(7x+12=4\)
9. \(-x-15=-14\)
10. \(15x+13=-7\)
11. \(-6x-11=-9\)
12. \(-9x-12=4\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-15}& = &5 \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15} & = &5\color{blue}{+15} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-15}& = &-8 \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+8}& = &11 \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-9}& = &-7 \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9} & = &-7\color{blue}{+9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+3}& = &14 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-15}& = &11 \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15} & = &11\color{blue}{+15} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-1}& = &-5 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+12}& = &4 \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12} & = &4\color{blue}{-12} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-15}& = &-14 \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15} & = &-14\color{blue}{+15} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+13}& = &-7 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-7\color{blue}{-13} \\\Leftrightarrow &15x & = &-20\\\Leftrightarrow & \color{red}{15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-11}& = &-9 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &-9\color{blue}{+11} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-12}& = &4 \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)