Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+1}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-14x } & = & -3 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+3}& = & 14 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+10x } & = & 14 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-13}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13+5x } & = & -4 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &13x & = &9\\\Leftrightarrow & \color{red}{13}x & = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+12}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+9x } & = & 10 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+15}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15+7x } & = & -1 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &22x & = &-16\\\Leftrightarrow & \color{red}{22}x & = &-16\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-16}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+2}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & 10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-14\\\Leftrightarrow & \color{red}{-11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-8x & = &28\\\Leftrightarrow & \color{red}{-8}x & = &28\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{28}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-5}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+11x } & = & 7 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &20x & = &12\\\Leftrightarrow & \color{red}{20}x & = &12\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{12}{20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)