Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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