Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-7}& = &12 \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &4x & = &19\\\Leftrightarrow & \color{red}{4}x & = &19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-12}& = &-2 \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12} & = &-2\color{blue}{+12} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = &7 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-4}& = &3 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &3\color{blue}{+4} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = &4 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = &-10 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &-10\color{blue}{+15} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-5}& = &-12 \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-7}& = &-12 \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7} & = &-12\color{blue}{+7} \\\Leftrightarrow &2x & = &-5\\\Leftrightarrow & \color{red}{2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+2}& = &15 \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-10}& = &14 \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &-15x & = &24\\\Leftrightarrow & \color{red}{-15}x & = &24\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{24}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-5}& = &-3 \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5} & = &-3\color{blue}{+5} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-7}& = &13 \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &12x & = &20\\\Leftrightarrow & \color{red}{12}x & = &20\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{20}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)