Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+10}& = &4 \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10} & = &4\color{blue}{-10} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-6}& = &-14 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-6}& = &6 \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6} & = &6\color{blue}{+6} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-4}& = &12 \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+4}& = &7 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &7\color{blue}{-4} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-2}& = &-1 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+1}& = &-11 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &-11\color{blue}{-1} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+15}& = &12 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-7}& = &-10 \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7} & = &-10\color{blue}{+7} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+14}& = &-3 \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14} & = &-3\color{blue}{-14} \\\Leftrightarrow &4x & = &-17\\\Leftrightarrow & \color{red}{4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-6}& = &-6 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &-6\color{blue}{+6} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+4}& = &-15 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)