Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-1}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+11x } & = & 5 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &26x & = &6\\\Leftrightarrow & \color{red}{26}x & = &6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-7x } & = & -7 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-5}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+2x } & = & -5 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-5}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-14x } & = & 8 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-23x & = &13\\\Leftrightarrow & \color{red}{-23}x & = &13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+6}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-5x } & = & -6 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+5}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-5x } & = & 12 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+2}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-7x } & = & 9 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-15}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-11x } & = & 1 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-21x & = &16\\\Leftrightarrow & \color{red}{-21}x & = &16\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{16}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{21} } & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)