Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+12}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+9x } & = & 9 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &14x & = &-3\\\Leftrightarrow & \color{red}{14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & -4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-6}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-7x } & = & 15 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-8}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x } & = & -12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+8} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-11}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+7x } & = & 15 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &18x & = &26\\\Leftrightarrow & \color{red}{18}x & = &26\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{26}{18} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &2x & = &-20\\\Leftrightarrow & \color{red}{2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)