Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-4)& = & 12 \color{red}{+} (7-5x) \\\Leftrightarrow & 3x-12& = &12+7-5x \\\Leftrightarrow & 3x \color{red}{-12} & = &19 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 3x+5x& = &19+12 \\\Leftrightarrow & 8x& = &31 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{31}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{31}{8} & & \\ & V = \left\{ \frac{31}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-5x+4)& = & -12 \color{red}{-} (14-2x) \\\Leftrightarrow & -15x+12& = &-12-14+2x \\\Leftrightarrow & -15x \color{red}{+12} & = &-26 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &-26 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & -15x-2x& = &-26-12 \\\Leftrightarrow & -17x& = &-38 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-38}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{38}{17} & & \\ & V = \left\{ \frac{38}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x+7)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & 12x+21& = &12-14+x \\\Leftrightarrow & 12x \color{red}{+21} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 12x-x& = &-2-21 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x+5)& = & 7 \color{red}{-} (-3-4x) \\\Leftrightarrow & 9x+15& = &7+3+4x \\\Leftrightarrow & 9x \color{red}{+15} & = &10 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 9x-4x& = &10-15 \\\Leftrightarrow & 5x& = &-5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-5}{ \color{red}{5} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (3x+7)& = & -1 \color{red}{+} (-1+2x) \\\Leftrightarrow & 15x+35& = &-1-1+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &-2-35 \\\Leftrightarrow & 13x& = &-37 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-37}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+2)& = & 8 \color{red}{+} (-15+2x) \\\Leftrightarrow & -15x+10& = &8-15+2x \\\Leftrightarrow & -15x \color{red}{+10} & = &-7 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & -15x-2x& = &-7-10 \\\Leftrightarrow & -17x& = &-17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-17}{ \color{red}{-17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-4)& = & -4 \color{red}{-} (-2+x) \\\Leftrightarrow & -30x-20& = &-4+2-x \\\Leftrightarrow & -30x \color{red}{-20} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -30x+x& = &-2+20 \\\Leftrightarrow & -29x& = &18 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{18}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-18}{29} & & \\ & V = \left\{ \frac{-18}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x-7)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & -18x-42& = &-9-10-x \\\Leftrightarrow & -18x \color{red}{-42} & = &-19 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -18x+x& = &-19+42 \\\Leftrightarrow & -17x& = &23 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{23}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-23}{17} & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-5x+3)& = & -12 \color{red}{-} (-11+3x) \\\Leftrightarrow & -20x+12& = &-12+11-3x \\\Leftrightarrow & -20x \color{red}{+12} & = &-1 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -20x+3x& = &-1-12 \\\Leftrightarrow & -17x& = &-13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{13}{17} & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-3)& = & -6 \color{red}{-} (4-2x) \\\Leftrightarrow & -15x-9& = &-6-4+2x \\\Leftrightarrow & -15x \color{red}{-9} & = &-10 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -15x-2x& = &-10+9 \\\Leftrightarrow & -17x& = &-1 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-1}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{1}{17} & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-4)& = & -5 \color{red}{-} (14+x) \\\Leftrightarrow & 30x-20& = &-5-14-x \\\Leftrightarrow & 30x \color{red}{-20} & = &-19 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &-19+20 \\\Leftrightarrow & 31x& = &1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{1}{31} & & \\ & V = \left\{ \frac{1}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x-7)& = & 11 \color{red}{+} (9-3x) \\\Leftrightarrow & -10x-14& = &11+9-3x \\\Leftrightarrow & -10x \color{red}{-14} & = &20 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -10x+3x& = &20+14 \\\Leftrightarrow & -7x& = &34 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{34}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-34}{7} & & \\ & V = \left\{ \frac{-34}{7} \right\} & \\\end{align}\)