Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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