Hard shifting into first and reverse gear is usually caused by a leaking hydraulic system that operates the clutch, resulting in the clutch disc not moving away from the spinning flywheel.
This can be checked by starting the car after engaging the gear and clutch, and if the vehicle stumbles forward, it should be taken to a servicing shop.
Other possible causes include a damaged master cylinder, low clutch fluid, damaged gears, and a damaged hub sleeve.
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Damaged Master Cylinder. The clutch system is comprised of a variety of components. There is the clutch master cylinder, the clutch cover (or pressure plate), the slave cylinder, the release fork, and the clutch release bearing (also called the throwout bearing).
Low Clutch Fluid. Like the braking system, most clutch systems use hydraulic fluid to transfer the force you apply to a pedal in the cabin. This force pushes on the clutch fork, which then pushes the pressure plate springs.
Damaged Gears. There are lots of gears in a manual transmission system. There is 1st gear, 2nd gear, 3rd gear, 4th gear, 5th gear, reverse gear, and sometimes a 6th or even 7th gear.
Damaged Hub Sleeve. When the hub gear bridges between the main gears, the hub sleeve (or synchronizer hub) is what actually engages these gears. It can move either right or left, depending on where the gear has shifted.
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