Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+14}& = &2 \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-2}& = &12 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &12\color{blue}{+2} \\\Leftrightarrow &7x & = &14\\\Leftrightarrow & \color{red}{7}x & = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-10}& = &-15 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-1}& = &13 \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1} & = &13\color{blue}{+1} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+15}& = &-1 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &-1\color{blue}{-15} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-7}& = &10 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &10\color{blue}{+7} \\\Leftrightarrow &6x & = &17\\\Leftrightarrow & \color{red}{6}x & = &17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-3}& = &7 \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3} & = &7\color{blue}{+3} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-12}& = &1 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &1\color{blue}{+12} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-9}& = &11 \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9} & = &11\color{blue}{+9} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-10}& = &11 \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+10}& = &-14 \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10} & = &-14\color{blue}{-10} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+8}& = &-2 \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)