Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+2}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-10x } & = & 10 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-19x & = &8\\\Leftrightarrow & \color{red}{-19}x & = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+1}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-9x } & = & 9 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-3}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-14x } & = & -7 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+9}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & -11 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-4}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-7x } & = & 10 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-5}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5-14x } & = & 11 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+7}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-13x } & = & -6 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+7}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-3x } & = & 13 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-15}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-13x } & = & 7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-27\\\Leftrightarrow & \color{red}{-5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{27}{5} } & & \\ & V = \left\{ \frac{27}{5} \right\} & \\\end{align}\)