Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+2}& = &-3 \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2} & = &-3\color{blue}{-2} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-9}& = &7 \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9} & = &7\color{blue}{+9} \\\Leftrightarrow &15x & = &16\\\Leftrightarrow & \color{red}{15}x & = &16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+8}& = &-13 \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+13}& = &-8 \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13} & = &-8\color{blue}{-13} \\\Leftrightarrow &4x & = &-21\\\Leftrightarrow & \color{red}{4}x & = &-21\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-21}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+12}& = &-11 \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12} & = &-11\color{blue}{-12} \\\Leftrightarrow &12x & = &-23\\\Leftrightarrow & \color{red}{12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-6}& = &7 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &-14x & = &13\\\Leftrightarrow & \color{red}{-14}x & = &13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{14} } & & \\ & V = \left\{ \frac{-13}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+8}& = &-4 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &-4\color{blue}{-8} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-14}& = &15 \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14} & = &15\color{blue}{+14} \\\Leftrightarrow &13x & = &29\\\Leftrightarrow & \color{red}{13}x & = &29\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{29}{13} \\\Leftrightarrow & \color{green}{ x = \frac{29}{13} } & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+3}& = &-10 \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+13}& = &5 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-11}& = &-8 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+8}& = &-1 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &-1\color{blue}{-8} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)