Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-4}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-11x } & = & -10 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-18x & = &-6\\\Leftrightarrow & \color{red}{-18}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+15}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+6x } & = & -2 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-5x } & = & -1 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-15}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-9x } & = & 12 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-x & = &27\\\Leftrightarrow & \color{red}{-}x & = &27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{27}{-1} \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-1}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-11x } & = & 3 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-21x & = &4\\\Leftrightarrow & \color{red}{-21}x & = &4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-10}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & -10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-12}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12+3x } & = & 1 \color{red}{ -3x }\color{blue}{+12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &10x & = &13\\\Leftrightarrow & \color{red}{10}x & = &13\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{13}{10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-13}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-9x } & = & 15 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &-2x & = &28\\\Leftrightarrow & \color{red}{-2}x & = &28\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{28}{-2} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+5}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & -14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-19\\\Leftrightarrow & \color{red}{-16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+10}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-11x } & = & 15 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)