Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-6}& = &-13 \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6} & = &-13\color{blue}{+6} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+13}& = &-14 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+4}& = &-13 \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4} & = &-13\color{blue}{-4} \\\Leftrightarrow &6x & = &-17\\\Leftrightarrow & \color{red}{6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+2}& = &3 \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-10}& = &1 \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10} & = &1\color{blue}{+10} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-5}& = &7 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+15}& = &14 \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15} & = &14\color{blue}{-15} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-14}& = &-14 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-13}& = &-6 \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13} & = &-6\color{blue}{+13} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+5}& = &-1 \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-11}& = &4 \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11} & = &4\color{blue}{+11} \\\Leftrightarrow &-10x & = &15\\\Leftrightarrow & \color{red}{-10}x & = &15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+6}& = &-8 \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6} & = &-8\color{blue}{-6} \\\Leftrightarrow &7x & = &-14\\\Leftrightarrow & \color{red}{7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-14}{7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)