Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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