Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-28\\\Leftrightarrow & \color{red}{-7}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-28}{-7} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+5}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-13x } & = & 4 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-18x & = &-1\\\Leftrightarrow & \color{red}{-18}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-1}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+5}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-8x } & = & 9 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+1}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-14x } & = & -7 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-11}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-11x } & = & 7 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-15}& = & -4 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & -4 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-x } & = & -1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-7x & = &14\\\Leftrightarrow & \color{red}{-7}x & = &14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{14}{-7} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+7}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-12x } & = & 4 \color{red}{ +12x }\color{blue}{-7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-23x & = &-3\\\Leftrightarrow & \color{red}{-23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+7}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-6x } & = & 1 \color{red}{ +6x }\color{blue}{-7-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)