Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+3}& = &-4 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &-4\color{blue}{-3} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-5}& = &15 \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+4}& = &-15 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &7x & = &-19\\\Leftrightarrow & \color{red}{7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+10}& = &12 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &12\color{blue}{-10} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+11}& = &-6 \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11} & = &-6\color{blue}{-11} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-3}& = &-3 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &-3\color{blue}{+3} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+10}& = &10 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &10\color{blue}{-10} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-12}& = &4 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &9x & = &16\\\Leftrightarrow & \color{red}{9}x & = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-15}& = &-5 \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15} & = &-5\color{blue}{+15} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-8}& = &-3 \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8} & = &-3\color{blue}{+8} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+10}& = &10 \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10} & = &10\color{blue}{-10} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+6}& = &-5 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-5\color{blue}{-6} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)