Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+4}& = &8 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &8\color{blue}{-4} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-10}& = &-6 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-6\color{blue}{+10} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-2}& = &7 \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-4}& = &5 \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4} & = &5\color{blue}{+4} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
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. \(\begin{align} & 15x \color{red}{+4}& = &3 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &3\color{blue}{-4} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-13}& = &14 \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13} & = &14\color{blue}{+13} \\\Leftrightarrow &11x & = &27\\\Leftrightarrow & \color{red}{11}x & = &27\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{27}{11} \\\Leftrightarrow & \color{green}{ x = \frac{27}{11} } & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-12}& = &13 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &4x & = &25\\\Leftrightarrow & \color{red}{4}x & = &25\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{25}{4} \\\Leftrightarrow & \color{green}{ x = \frac{25}{4} } & & \\ & V = \left\{ \frac{25}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+12}& = &1 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &1\color{blue}{-12} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-11}& = &12 \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &11x & = &23\\\Leftrightarrow & \color{red}{11}x & = &23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+7}& = &-14 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &-14\color{blue}{-7} \\\Leftrightarrow &8x & = &-21\\\Leftrightarrow & \color{red}{8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-10}& = &-9 \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10} & = &-9\color{blue}{+10} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)