Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+4}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+7x } & = & 4 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &22x & = &0\\\Leftrightarrow & \color{red}{22}x & = &0\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{0}{22} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-9x } & = & 8 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 8 \color{blue}{-1} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+3}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+11x } & = & -4 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+4}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-8x } & = & -5 \color{red}{ +8x }\color{blue}{-4-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-23x & = &-9\\\Leftrightarrow & \color{red}{-23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+9}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-13x } & = & 5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &x & = &10\\\Leftrightarrow & \color{red}{}x & = &10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 10 \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-1}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1+13x } & = & 1 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &27x & = &2\\\Leftrightarrow & \color{red}{27}x & = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-22\\\Leftrightarrow & \color{red}{-9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-6}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-5x } & = & 5 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)