Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+8}& = &14 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+11}& = &-9 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &-9\color{blue}{-11} \\\Leftrightarrow &12x & = &-20\\\Leftrightarrow & \color{red}{12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+9}& = &9 \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9} & = &9\color{blue}{-9} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+10}& = &-8 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-1}& = &14 \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-8}& = &-4 \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+2}& = &2 \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2} & = &2\color{blue}{-2} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-11}& = &-2 \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+11}& = &-4 \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &10x & = &-15\\\Leftrightarrow & \color{red}{10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+13}& = &-10 \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13} & = &-10\color{blue}{-13} \\\Leftrightarrow &-15x & = &-23\\\Leftrightarrow & \color{red}{-15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{23}{15} } & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+9}& = &14 \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9} & = &14\color{blue}{-9} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+14}& = &-8 \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14} & = &-8\color{blue}{-14} \\\Leftrightarrow &-12x & = &-22\\\Leftrightarrow & \color{red}{-12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)