Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+15}& = &3 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+1}& = &1 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-14}& = &-6 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &-6\color{blue}{+14} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-5}& = &15 \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-1}& = &-2 \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+15}& = &13 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &13\color{blue}{-15} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-5}& = &2 \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5} & = &2\color{blue}{+5} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+2}& = &-2 \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2} & = &-2\color{blue}{-2} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+1}& = &6 \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1} & = &6\color{blue}{-1} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+8}& = &-4 \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8} & = &-4\color{blue}{-8} \\\Leftrightarrow &-2x & = &-12\\\Leftrightarrow & \color{red}{-2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-12}{-2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+4}& = &2 \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4} & = &2\color{blue}{-4} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+5}& = &-6 \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)