Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-9}& = & -15 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-15x } & = & -15 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-11x } & = & -13 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-20\\\Leftrightarrow & \color{red}{-10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-20}{-10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-5}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-13x } & = & 5 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & 2 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+7}& = & 4 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+10x } & = & 4 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+8}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-4x } & = & -5 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+3}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-13x } & = & 15 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-28x & = &12\\\Leftrightarrow & \color{red}{-28}x & = &12\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{12}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+5}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5-5x } & = & 8 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+11}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-14x } & = & -12 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &-27x & = &-23\\\Leftrightarrow & \color{red}{-27}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{23}{27} } & & \\ & V = \left\{ \frac{23}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-11}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+13x } & = & -11 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &22x & = &0\\\Leftrightarrow & \color{red}{22}x & = &0\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{0}{22} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)