Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = &-14 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &14x & = &-23\\\Leftrightarrow & \color{red}{14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+1}& = &1 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-2}& = &-12 \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = &14 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+13}& = &5 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+2}& = &13 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &13\color{blue}{-2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-15}& = &-13 \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15} & = &-13\color{blue}{+15} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+3}& = &12 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3} & = &12\color{blue}{-3} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+10}& = &-13 \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10} & = &-13\color{blue}{-10} \\\Leftrightarrow &-x & = &-23\\\Leftrightarrow & \color{red}{-}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-23}{-1} \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+1}& = &-14 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &-14\color{blue}{-1} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+4}& = &15 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &15\color{blue}{-4} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-15}& = &5 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &5\color{blue}{+15} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)