Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-1}& = &-15 \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1} & = &-15\color{blue}{+1} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-15}& = &5 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &5\color{blue}{+15} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-1}& = &11 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &11\color{blue}{+1} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+11}& = &-12 \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11} & = &-12\color{blue}{-11} \\\Leftrightarrow &2x & = &-23\\\Leftrightarrow & \color{red}{2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-23}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+11}& = &7 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &7\color{blue}{-11} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-1}& = &2 \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1} & = &2\color{blue}{+1} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+10}& = &-9 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &-9\color{blue}{-10} \\\Leftrightarrow &5x & = &-19\\\Leftrightarrow & \color{red}{5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-2}& = &-1 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-4}& = &10 \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+11}& = &13 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &13\color{blue}{-11} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-12}& = &4 \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+9}& = &7 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &7\color{blue}{-9} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)