Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-10}& = &9 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &9\color{blue}{+10} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-11}& = &5 \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-4}& = &11 \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4} & = &11\color{blue}{+4} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+6}& = &12 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &12\color{blue}{-6} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+7}& = &5 \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+12}& = &-6 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-6\color{blue}{-12} \\\Leftrightarrow &6x & = &-18\\\Leftrightarrow & \color{red}{6}x & = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = &10 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &10\color{blue}{-7} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-6}& = &12 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &12\color{blue}{+6} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+7}& = &-10 \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7} & = &-10\color{blue}{-7} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-1}& = &12 \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1} & = &12\color{blue}{+1} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-15}& = &6 \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-9}& = &2 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)