Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+1)& = & 3 \color{red}{-} (4-2x) \\\Leftrightarrow & 15x+3& = &3-4+2x \\\Leftrightarrow & 15x \color{red}{+3} & = &-1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & 15x-2x& = &-1-3 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x-2)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & 15x-6& = &10+13-x \\\Leftrightarrow & 15x \color{red}{-6} & = &23 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 15x+x& = &23+6 \\\Leftrightarrow & 16x& = &29 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{29}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{29}{16} & & \\ & V = \left\{ \frac{29}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-4x-7)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & -8x-14& = &8+11+x \\\Leftrightarrow & -8x \color{red}{-14} & = &19 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -8x-x& = &19+14 \\\Leftrightarrow & -9x& = &33 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{33}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-6)& = & -4 \color{red}{-} (15+x) \\\Leftrightarrow & 12x-12& = &-4-15-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-19 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-19+12 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-6)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-24& = &-1-8-x \\\Leftrightarrow & 12x \color{red}{-24} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &-9+24 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x-1)& = & -8 \color{red}{+} (11-3x) \\\Leftrightarrow & -4x-2& = &-8+11-3x \\\Leftrightarrow & -4x \color{red}{-2} & = &3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & -4x+3x& = &3+2 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+4)& = & 2 \color{red}{+} (-3-5x) \\\Leftrightarrow & -6x+8& = &2-3-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &-1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &-1-8 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+4)& = & -3 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+16& = &-3-3-x \\\Leftrightarrow & -12x \color{red}{+16} & = &-6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -12x+x& = &-6-16 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+6)& = & -12 \color{red}{+} (15+x) \\\Leftrightarrow & -2x+12& = &-12+15+x \\\Leftrightarrow & -2x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -2x-x& = &3-12 \\\Leftrightarrow & -3x& = &-9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-9}{ \color{red}{-3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+3)& = & 7 \color{red}{-} (5+x) \\\Leftrightarrow & 20x+12& = &7-5-x \\\Leftrightarrow & 20x \color{red}{+12} & = &2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 20x+x& = &2-12 \\\Leftrightarrow & 21x& = &-10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-7)& = & -6 \color{red}{-} (15+x) \\\Leftrightarrow & -24x-28& = &-6-15-x \\\Leftrightarrow & -24x \color{red}{-28} & = &-21 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &-21+28 \\\Leftrightarrow & -23x& = &7 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{7}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x+2)& = & -12 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x+4& = &-12+4-5x \\\Leftrightarrow & -6x \color{red}{+4} & = &-8 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -6x+5x& = &-8-4 \\\Leftrightarrow & -x& = &-12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-12}{ \color{red}{-1} } \\\Leftrightarrow & x = 12 & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)