Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+10}& = &-10 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &-10x & = &-20\\\Leftrightarrow & \color{red}{-10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-20}{-10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+4}& = &9 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &9\color{blue}{-4} \\\Leftrightarrow &4x & = &5\\\Leftrightarrow & \color{red}{4}x & = &5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+12}& = &-11 \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12} & = &-11\color{blue}{-12} \\\Leftrightarrow &15x & = &-23\\\Leftrightarrow & \color{red}{15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-23}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+8}& = &1 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &1\color{blue}{-8} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+14}& = &-15 \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14} & = &-15\color{blue}{-14} \\\Leftrightarrow &-x & = &-29\\\Leftrightarrow & \color{red}{-}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-2}& = &-6 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+12}& = &7 \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-11}& = &14 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &10x & = &25\\\Leftrightarrow & \color{red}{10}x & = &25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-3}& = &11 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &11\color{blue}{+3} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+7}& = &1 \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7} & = &1\color{blue}{-7} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+4}& = &-7 \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+6}& = &-11 \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6} & = &-11\color{blue}{-6} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)