Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-7}& = & -9 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7+6x } & = & -9 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-9}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+2x } & = & 1 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-1}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-6x } & = & 8 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-5}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+7x } & = & 3 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &22x & = &8\\\Leftrightarrow & \color{red}{22}x & = &8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-x } & = & -14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &12x & = &-24\\\Leftrightarrow & \color{red}{12}x & = &-24\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-24}{12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-15}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-9x } & = & 7 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)