Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+7)& = & -9 \color{red}{+} (8-4x) \\\Leftrightarrow & -9x+21& = &-9+8-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &-1-21 \\\Leftrightarrow & -5x& = &-22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{22}{5} & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-7)& = & -6 \color{red}{-} (-8+x) \\\Leftrightarrow & 36x-42& = &-6+8-x \\\Leftrightarrow & 36x \color{red}{-42} & = &2 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 36x+x& = &2+42 \\\Leftrightarrow & 37x& = &44 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{44}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{44}{37} & & \\ & V = \left\{ \frac{44}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x+5)& = & -9 \color{red}{+} (10+4x) \\\Leftrightarrow & 3x+15& = &-9+10+4x \\\Leftrightarrow & 3x \color{red}{+15} & = &1 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 3x-4x& = &1-15 \\\Leftrightarrow & -x& = &-14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-14}{ \color{red}{-1} } \\\Leftrightarrow & x = 14 & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x+7)& = & 7 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x+42& = &7+8-x \\\Leftrightarrow & 12x \color{red}{+42} & = &15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 12x+x& = &15-42 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-3x+3)& = & 12 \color{red}{+} (-11+2x) \\\Leftrightarrow & -15x+15& = &12-11+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &1 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &1-15 \\\Leftrightarrow & -17x& = &-14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-5)& = & 12 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-20& = &12+8-x \\\Leftrightarrow & -24x \color{red}{-20} & = &20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -24x+x& = &20+20 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x-5)& = & 8 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-20& = &8-6+x \\\Leftrightarrow & -12x \color{red}{-20} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -12x-x& = &2+20 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x+6)& = & 13 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x+24& = &13+6-x \\\Leftrightarrow & -24x \color{red}{+24} & = &19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &19-24 \\\Leftrightarrow & -23x& = &-5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-6)& = & 10 \color{red}{-} (7+x) \\\Leftrightarrow & -18x-18& = &10-7-x \\\Leftrightarrow & -18x \color{red}{-18} & = &3 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -18x+x& = &3+18 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (6x-2)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & 30x-10& = &-4-12-x \\\Leftrightarrow & 30x \color{red}{-10} & = &-16 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 30x+x& = &-16+10 \\\Leftrightarrow & 31x& = &-6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-6}{31} & & \\ & V = \left\{ \frac{-6}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x+4)& = & 4 \color{red}{+} (-3-4x) \\\Leftrightarrow & -25x+20& = &4-3-4x \\\Leftrightarrow & -25x \color{red}{+20} & = &1 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -25x+4x& = &1-20 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x+7)& = & 12 \color{red}{-} (-12+x) \\\Leftrightarrow & 20x+35& = &12+12-x \\\Leftrightarrow & 20x \color{red}{+35} & = &24 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 20x+x& = &24-35 \\\Leftrightarrow & 21x& = &-11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)