Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-5}& = &15 \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-12}& = &-3 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-11}& = &-2 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-12}& = &-8 \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-3}& = &6 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+10}& = &-4 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &-4\color{blue}{-10} \\\Leftrightarrow &14x & = &-14\\\Leftrightarrow & \color{red}{14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-14}{14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+7}& = &14 \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7} & = &14\color{blue}{-7} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+9}& = &-15 \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9} & = &-15\color{blue}{-9} \\\Leftrightarrow &7x & = &-24\\\Leftrightarrow & \color{red}{7}x & = &-24\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-24}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = &3 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &3\color{blue}{-11} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+2}& = &14 \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2} & = &14\color{blue}{-2} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-12}& = &-12 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-1}& = &10 \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1} & = &10\color{blue}{+1} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)