Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-x } & = & -6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & -8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-1}& = & 12 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-2x } & = & 12 \color{red}{ +2x }\color{blue}{+1-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-12x & = &26\\\Leftrightarrow & \color{red}{-12}x & = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+1}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1+13x } & = & -3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &27x & = &-4\\\Leftrightarrow & \color{red}{27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-10}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x } & = & 1 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-28x & = &11\\\Leftrightarrow & \color{red}{-28}x & = &11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{28} } & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+12}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & -8 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+3}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-11x } & = & -3 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+15}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-11x } & = & 4 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-18x & = &-11\\\Leftrightarrow & \color{red}{-18}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{11}{18} } & & \\ & V = \left\{ \frac{11}{18} \right\} & \\\end{align}\)