Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+6}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-11x } & = & 6 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+12}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-7x } & = & 4 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-20x & = &-8\\\Leftrightarrow & \color{red}{-20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & 10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-5}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-11x } & = & 7 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-11}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11+7x } & = & -6 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &15x & = &5\\\Leftrightarrow & \color{red}{15}x & = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-1}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-8x } & = & -4 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-x } & = & 13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-1}& = & -15 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1+6x } & = & -15 \color{red}{ -6x }\color{blue}{+1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &19x & = &-14\\\Leftrightarrow & \color{red}{19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+6}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-13x } & = & 10 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-28x & = &4\\\Leftrightarrow & \color{red}{-28}x & = &4\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{4}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-3}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-13x } & = & -9 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+15}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-10x } & = & 7 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-x & = &-8\\\Leftrightarrow & \color{red}{-}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-8}{-1} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+15}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-13x } & = & 10 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-28x & = &-5\\\Leftrightarrow & \color{red}{-28}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{5}{28} } & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)