Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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