Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-20} & = & \color{red}{-154x} +77 \\\Leftrightarrow & -220x \color{red}{-20} \color{blue}{+20} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+20} \\\Leftrightarrow & -220x+154x& = & 77+20 \\\Leftrightarrow & \color{red}{-66} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-66} & & \\\Leftrightarrow & x = \frac{-97}{66} & & \\ & V = \left\{ \frac{-97}{66} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-66} & = & \color{red}{385x} +10 \\\Leftrightarrow & -550x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -550x-385x& = & 10+66 \\\Leftrightarrow & \color{red}{-935} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-935} & & \\\Leftrightarrow & x = \frac{-76}{935} & & \\ & V = \left\{ \frac{-76}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -8x+\frac{2}{11} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{-165} & = & \color{red}{-352x} +8 \\\Leftrightarrow & 660x \color{red}{-165} \color{blue}{+165} \color{blue}{+352x} & = & \color{red}{-352x} +8 \color{blue}{+352x} \color{blue}{+165} \\\Leftrightarrow & 660x+352x& = & 8+165 \\\Leftrightarrow & \color{red}{1012} x& = & 173 \\\Leftrightarrow & x = \frac{173}{1012} & & \\ & V = \left\{ \frac{173}{1012} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-56} & = & \color{red}{441x} +36 \\\Leftrightarrow & 1260x \color{red}{-56} \color{blue}{+56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{+56} \\\Leftrightarrow & 1260x-441x& = & 36+56 \\\Leftrightarrow & \color{red}{819} x& = & 92 \\\Leftrightarrow & x = \frac{92}{819} & & \\ & V = \left\{ \frac{92}{819} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{24}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+72} \\\Leftrightarrow & 792x+165x& = & 22+72 \\\Leftrightarrow & \color{red}{957} x& = & 94 \\\Leftrightarrow & x = \frac{94}{957} & & \\ & V = \left\{ \frac{94}{957} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{15}{8}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{80}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 80x \color{red}{+15} & = & \color{red}{-56x} +12 \\\Leftrightarrow & 80x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +12 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & 80x+56x& = & 12-15 \\\Leftrightarrow & \color{red}{136} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{136} & & \\ & V = \left\{ \frac{-3}{136} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -20x-\frac{20}{9}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-20} & = & \color{red}{-63x} +7 \\\Leftrightarrow & -180x \color{red}{-20} \color{blue}{+20} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{+20} \\\Leftrightarrow & -180x+63x& = & 7+20 \\\Leftrightarrow & \color{red}{-117} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-117} & & \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{15}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x- \frac{150}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{-150} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -1100x \color{red}{-150} \color{blue}{+150} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{+150} \\\Leftrightarrow & -1100x+770x& = & 99+150 \\\Leftrightarrow & \color{red}{-330} x& = & 249 \\\Leftrightarrow & x = \frac{249}{-330} & & \\\Leftrightarrow & x = \frac{-83}{110} & & \\ & V = \left\{ \frac{-83}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{9})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{16}{9}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{16}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{81x} +30 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{-81x} & = & \color{red}{81x} +30 \color{blue}{-81x} \color{blue}{+16} \\\Leftrightarrow & -72x-81x& = & 30+16 \\\Leftrightarrow & \color{red}{-153} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-153} & & \\\Leftrightarrow & x = \frac{-46}{153} & & \\ & V = \left\{ \frac{-46}{153} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -14x-\frac{28}{3}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-308} & = & \color{red}{99x} +18 \\\Leftrightarrow & -462x \color{red}{-308} \color{blue}{+308} \color{blue}{-99x} & = & \color{red}{99x} +18 \color{blue}{-99x} \color{blue}{+308} \\\Leftrightarrow & -462x-99x& = & 18+308 \\\Leftrightarrow & \color{red}{-561} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-561} & & \\\Leftrightarrow & x = \frac{-326}{561} & & \\ & V = \left\{ \frac{-326}{561} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{9}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-45} & = & \color{red}{245x} +14 \\\Leftrightarrow & -210x \color{red}{-45} \color{blue}{+45} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{+45} \\\Leftrightarrow & -210x-245x& = & 14+45 \\\Leftrightarrow & \color{red}{-455} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-455} & & \\\Leftrightarrow & x = \frac{-59}{455} & & \\ & V = \left\{ \frac{-59}{455} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{231x} +21 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 495x-231x& = & 21-220 \\\Leftrightarrow & \color{red}{264} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{264} & & \\ & V = \left\{ \frac{-199}{264} \right\} & \\\end{align}\)