Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+14}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-11x } & = & 2 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-21x & = &-12\\\Leftrightarrow & \color{red}{-21}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-12}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+3}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & 7 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-12}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+12x } & = & -15 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &25x & = &-3\\\Leftrightarrow & \color{red}{25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-8}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & 4 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-x } & = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-5}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+4x } & = & -1 \color{red}{ -4x }\color{blue}{+5+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+9}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-4x } & = & -1 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+2}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2-2x } & = & -10 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-12\\\Leftrightarrow & \color{red}{-3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-12}{-3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-13x & = &28\\\Leftrightarrow & \color{red}{-13}x & = &28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)