Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+14}& = &14 \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14} & = &14\color{blue}{-14} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-10}& = &6 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &6\color{blue}{+10} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+11}& = &-6 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &-6\color{blue}{-11} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-15}& = &15 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &4x & = &30\\\Leftrightarrow & \color{red}{4}x & = &30\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{30}{4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-10}& = &15 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-5}& = &2 \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5} & = &2\color{blue}{+5} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-2}& = &8 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+13}& = &-5 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13} & = &-5\color{blue}{-13} \\\Leftrightarrow &-12x & = &-18\\\Leftrightarrow & \color{red}{-12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+5}& = &-8 \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+15}& = &-11 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &-13x & = &-26\\\Leftrightarrow & \color{red}{-13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-26}{-13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+6}& = &-8 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &-8\color{blue}{-6} \\\Leftrightarrow &-2x & = &-14\\\Leftrightarrow & \color{red}{-2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-14}{-2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+15}& = &15 \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)