Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+14}& = &-14 \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &-10x & = &-28\\\Leftrightarrow & \color{red}{-10}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-28}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+8}& = &-13 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &-12x & = &-21\\\Leftrightarrow & \color{red}{-12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = &4 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &4\color{blue}{-9} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+11}& = &-4 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+7}& = &15 \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-9}& = &3 \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-1}& = &6 \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &6x & = &7\\\Leftrightarrow & \color{red}{6}x & = &7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+12}& = &-1 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+12}& = &-14 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &-14\color{blue}{-12} \\\Leftrightarrow &-13x & = &-26\\\Leftrightarrow & \color{red}{-13}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-26}{-13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-12}& = &-9 \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-12}& = &-8 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &-8\color{blue}{+12} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-2}& = &13 \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)