Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+11}& = &7 \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11} & = &7\color{blue}{-11} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+5}& = &5 \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+1}& = &2 \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+5}& = &6 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &6\color{blue}{-5} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-9}& = &-1 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-2}& = &-6 \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+1}& = &-2 \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1} & = &-2\color{blue}{-1} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+1}& = &-13 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &-13\color{blue}{-1} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+5}& = &10 \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5} & = &10\color{blue}{-5} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+3}& = &7 \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3} & = &7\color{blue}{-3} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-12}& = &-3 \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-9}& = &13 \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9} & = &13\color{blue}{+9} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)