Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-9}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+7x } & = & -13 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &22x & = &-4\\\Leftrightarrow & \color{red}{22}x & = &-4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+5}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-11x } & = & -15 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-3}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-9x } & = & -10 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-9}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+7x } & = & -12 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &18x & = &-3\\\Leftrightarrow & \color{red}{18}x & = &-3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-9}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-13x } & = & 8 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-10x } & = & 1 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-14}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-13x } & = & 1 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-10}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-3x } & = & -6 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -6 \color{blue}{+10} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)