Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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