Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+5}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-8x } & = & -3 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 15 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+15}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & -12 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &23x & = &-27\\\Leftrightarrow & \color{red}{23}x & = &-27\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-27}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{23} } & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+7}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+9x } & = & 11 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &19x & = &4\\\Leftrightarrow & \color{red}{19}x & = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & -14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-28\\\Leftrightarrow & \color{red}{-4}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-28}{-4} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & 15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-3}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-7x } & = & 11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & -15 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)