Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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