Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-9}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-5x } & = & 2 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+1}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-5x } & = & 3 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-5}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-11x } & = & 2 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-2x & = &7\\\Leftrightarrow & \color{red}{-2}x & = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-4}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-2x } & = & 1 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-12}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-10x } & = & -6 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+4}& = & 15 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4-2x } & = & 15 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+15}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+2x } & = & 7 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)