Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+6}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+7x } & = & 9 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &22x & = &3\\\Leftrightarrow & \color{red}{22}x & = &3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{3}{22} } & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+7}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-9x } & = & -4 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-1}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-7x } & = & -1 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+11}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11+11x } & = & -3 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-7x } & = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-10}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+11x } & = & 5 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &17x & = &15\\\Leftrightarrow & \color{red}{17}x & = &15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+2}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-10x } & = & -14 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)