Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & -9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-1}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1+11x } & = & -10 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+7}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-6x } & = & 6 \color{red}{ +6x }\color{blue}{-7-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-1}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-11x } & = & 7 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-21x & = &8\\\Leftrightarrow & \color{red}{-21}x & = &8\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{8}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{21} } & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & -9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-10}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & -9 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-27x & = &1\\\Leftrightarrow & \color{red}{-27}x & = &1\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{1}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{27} } & & \\ & V = \left\{ \frac{-1}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+13}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-13x } & = & -5 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+14x } & = & -5 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &29x & = &-16\\\Leftrightarrow & \color{red}{29}x & = &-16\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-16}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{29} } & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+1}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-5x } & = & 13 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)