Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-5)& = & 5 \color{red}{-} (13+3x) \\\Leftrightarrow & 20x-20& = &5-13-3x \\\Leftrightarrow & 20x \color{red}{-20} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 20x+3x& = &-8+20 \\\Leftrightarrow & 23x& = &12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+5)& = & -9 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+15& = &-9-5+x \\\Leftrightarrow & -12x \color{red}{+15} & = &-14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -12x-x& = &-14-15 \\\Leftrightarrow & -13x& = &-29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{29}{13} & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+3)& = & -4 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x+18& = &-4-11+x \\\Leftrightarrow & 24x \color{red}{+18} & = &-15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 24x-x& = &-15-18 \\\Leftrightarrow & 23x& = &-33 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-33}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-33}{23} & & \\ & V = \left\{ \frac{-33}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x+4)& = & 4 \color{red}{-} (1+3x) \\\Leftrightarrow & -5x+20& = &4-1-3x \\\Leftrightarrow & -5x \color{red}{+20} & = &3 \color{red}{-3x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -5x+3x& = &3-20 \\\Leftrightarrow & -2x& = &-17 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-17}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{17}{2} & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-7)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & -24x-42& = &2+10+x \\\Leftrightarrow & -24x \color{red}{-42} & = &12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &12+42 \\\Leftrightarrow & -25x& = &54 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{54}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-54}{25} & & \\ & V = \left\{ \frac{-54}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-4)& = & -6 \color{red}{+} (-1-2x) \\\Leftrightarrow & -3x-12& = &-6-1-2x \\\Leftrightarrow & -3x \color{red}{-12} & = &-7 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -3x+2x& = &-7+12 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-5)& = & 9 \color{red}{-} (14+x) \\\Leftrightarrow & 20x-25& = &9-14-x \\\Leftrightarrow & 20x \color{red}{-25} & = &-5 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 20x+x& = &-5+25 \\\Leftrightarrow & 21x& = &20 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{20}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x+6)& = & 12 \color{red}{-} (10-5x) \\\Leftrightarrow & -36x+36& = &12-10+5x \\\Leftrightarrow & -36x \color{red}{+36} & = &2 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -36x-5x& = &2-36 \\\Leftrightarrow & -41x& = &-34 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-34}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{34}{41} & & \\ & V = \left\{ \frac{34}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x+4)& = & 14 \color{red}{-} (-13+x) \\\Leftrightarrow & -9x+12& = &14+13-x \\\Leftrightarrow & -9x \color{red}{+12} & = &27 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -9x+x& = &27-12 \\\Leftrightarrow & -8x& = &15 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{15}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-15}{8} & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x+5)& = & -1 \color{red}{+} (7+3x) \\\Leftrightarrow & -20x+25& = &-1+7+3x \\\Leftrightarrow & -20x \color{red}{+25} & = &6 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & -20x-3x& = &6-25 \\\Leftrightarrow & -23x& = &-19 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-19}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x+2)& = & -13 \color{red}{+} (13-5x) \\\Leftrightarrow & 16x+8& = &-13+13-5x \\\Leftrightarrow & 16x \color{red}{+8} & = &0 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 16x+5x& = &0-8 \\\Leftrightarrow & 21x& = &-8 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-8}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x-5)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 8x-10& = &2-2-x \\\Leftrightarrow & 8x \color{red}{-10} & = &0 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 8x+x& = &0+10 \\\Leftrightarrow & 9x& = &10 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{10}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{10}{9} & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)