Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{5})& = & 3x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{8}{5}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-88} & = & \color{red}{165x} +40 \\\Leftrightarrow & 440x \color{red}{-88} \color{blue}{+88} \color{blue}{-165x} & = & \color{red}{165x} +40 \color{blue}{-165x} \color{blue}{+88} \\\Leftrightarrow & 440x-165x& = & 40+88 \\\Leftrightarrow & \color{red}{275} x& = & 128 \\\Leftrightarrow & x = \frac{128}{275} & & \\ & V = \left\{ \frac{128}{275} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{11})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 21x+\frac{28}{11}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x+ \frac{84}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{+84} & = & \color{red}{-66x} +110 \\\Leftrightarrow & 693x \color{red}{+84} \color{blue}{-84} \color{blue}{+66x} & = & \color{red}{-66x} +110 \color{blue}{+66x} \color{blue}{-84} \\\Leftrightarrow & 693x+66x& = & 110-84 \\\Leftrightarrow & \color{red}{759} x& = & 26 \\\Leftrightarrow & x = \frac{26}{759} & & \\ & V = \left\{ \frac{26}{759} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{15}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-30} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -280x \color{red}{-30} \color{blue}{+30} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{+30} \\\Leftrightarrow & -280x+126x& = & 21+30 \\\Leftrightarrow & \color{red}{-154} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-154} & & \\\Leftrightarrow & x = \frac{-51}{154} & & \\ & V = \left\{ \frac{-51}{154} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+20} & = & \color{red}{154x} +99 \\\Leftrightarrow & -220x \color{red}{+20} \color{blue}{-20} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-20} \\\Leftrightarrow & -220x-154x& = & 99-20 \\\Leftrightarrow & \color{red}{-374} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-374} & & \\\Leftrightarrow & x = \frac{-79}{374} & & \\ & V = \left\{ \frac{-79}{374} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 8x+\frac{7}{6} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 8x+\frac{7}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{14}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 108x \color{red}{-45} & = & \color{red}{96x} +14 \\\Leftrightarrow & 108x \color{red}{-45} \color{blue}{+45} \color{blue}{-96x} & = & \color{red}{96x} +14 \color{blue}{-96x} \color{blue}{+45} \\\Leftrightarrow & 108x-96x& = & 14+45 \\\Leftrightarrow & \color{red}{12} x& = & 59 \\\Leftrightarrow & x = \frac{59}{12} & & \\ & V = \left\{ \frac{59}{12} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 35x+\frac{35}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+35} & = & \color{red}{33x} +4 \\\Leftrightarrow & 385x \color{red}{+35} \color{blue}{-35} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{-35} \\\Leftrightarrow & 385x-33x& = & 4-35 \\\Leftrightarrow & \color{red}{352} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{352} & & \\ & V = \left\{ \frac{-31}{352} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -300x+135x& = & 50+36 \\\Leftrightarrow & \color{red}{-165} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-165} & & \\\Leftrightarrow & x = \frac{-86}{165} & & \\ & V = \left\{ \frac{-86}{165} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{90x} +45 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{+24} \\\Leftrightarrow & -80x-90x& = & 45+24 \\\Leftrightarrow & \color{red}{-170} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-170} & & \\\Leftrightarrow & x = \frac{-69}{170} & & \\ & V = \left\{ \frac{-69}{170} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{10})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{9}{10}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{+27} & = & \color{red}{210x} +40 \\\Leftrightarrow & -180x \color{red}{+27} \color{blue}{-27} \color{blue}{-210x} & = & \color{red}{210x} +40 \color{blue}{-210x} \color{blue}{-27} \\\Leftrightarrow & -180x-210x& = & 40-27 \\\Leftrightarrow & \color{red}{-390} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-390} & & \\\Leftrightarrow & x = \frac{-1}{30} & & \\ & V = \left\{ \frac{-1}{30} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{4})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 28x-\frac{21}{4}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{784}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 784x \color{red}{-147} & = & \color{red}{-140x} +24 \\\Leftrightarrow & 784x \color{red}{-147} \color{blue}{+147} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{+147} \\\Leftrightarrow & 784x+140x& = & 24+147 \\\Leftrightarrow & \color{red}{924} x& = & 171 \\\Leftrightarrow & x = \frac{171}{924} & & \\\Leftrightarrow & x = \frac{57}{308} & & \\ & V = \left\{ \frac{57}{308} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+56} & = & \color{red}{441x} +36 \\\Leftrightarrow & -378x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -378x-441x& = & 36-56 \\\Leftrightarrow & \color{red}{-819} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-819} & & \\\Leftrightarrow & x = \frac{20}{819} & & \\ & V = \left\{ \frac{20}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & -5x+\frac{5}{4} \\\Leftrightarrow & 4x+\frac{10}{3}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{+40} & = & \color{red}{-60x} +15 \\\Leftrightarrow & 48x \color{red}{+40} \color{blue}{-40} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{-40} \\\Leftrightarrow & 48x+60x& = & 15-40 \\\Leftrightarrow & \color{red}{108} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{108} & & \\ & V = \left\{ \frac{-25}{108} \right\} & \\\end{align}\)