Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-6}& = & -7 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-15x } & = & -7 \color{red}{ +15x }\color{blue}{+6-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+9}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-11x } & = & -2 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-21x & = &-11\\\Leftrightarrow & \color{red}{-21}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-11}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{11}{21} } & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+2}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+5x } & = & 6 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-4}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-5x } & = & 4 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+15}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+3x } & = & 5 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-15}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x } & = & -11 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-18x & = &4\\\Leftrightarrow & \color{red}{-18}x & = &4\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{4}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-15}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-7x } & = & 2 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-7}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+11x } & = & 4 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-14}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-7x } & = & -9 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &8x & = &5\\\Leftrightarrow & \color{red}{8}x & = &5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)